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The excited states of ¹⁶⁰DY Azodi, Hormoz 1974

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THE EXCITED STATES OF Dy by HORMOZ AZODI B.Sc. Washington State University 1971 A THESIS SUBMITTED IN PARTIAL FUIJTXLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July,1974 In presenting th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree l y ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho lar l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my wri t ten permission. Department The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Abstract i i The gamma-rays and the conversion electrons emitted following the beta decay of ^ ^Tb—*• "^Dy have been studied using Ge(Li) and S i ( L i ) detectors. The measured energies and i n t e n s i t i e s of these t r a n s i t i o n s , together with the re s u l t s of gamma-gamma coincidence measurements, have allowed us to construct the decay scheme of "^Dy. Four new trans i t i o n s , namely 97.7$ 111.8, 148.5 and 320.5 kev, are placed i n the decay scheme on the basis of energy f i t and coincidence r e s u l t s . The angular momentum and the parity of the excited states of t h i s nucleus have been deduced as confirmations of previous assignments. The energies and the electromagnetic properties of these states are compared to the predictions of the theory of a r i g i d asymmetric rotor. Table of Contents i l l Abstract n List of Tables v List of Figures vi Acknowledgements v i i Chapter I Introduction 1 Chapter II Collective Model of Even-Even Deformed Nuclei 4 2- The Asymmetric Rigid Rotor Model 7 3- Theory of Odd Parity States 10 4- Reduced E2 Branching Ratios 13 Chapter III Gamma-Ray Singles Spectroscopy 15 1- Peak Fitting 15 2- Energy Calibration 18 3- Efficiency Calibration 21 4- ^ Opb Gamma Spectrum 26 5- Sum Peaks 37 Chapter IV K-Conversion Electrons 48 1- K-Conversion Electrons in Coincidence with K-X-Rays 49 Chapter V Gamma-Gamma Coincidence Spectroscopy 59 1- Coincidence Data from Sum Peaks 59 2- Experimental Procedure 62 l60 3- Coincidence Measurements for Dy 68 Chapter VI Results and Model Comparisons 83 1- Spin Assignments and Branching Ratios 85 2- Model Fitting for the Positive Parity Levels 94 3- Model Fitting for the Odd Parity States 96 4- Conclusions References List of Tables v Chapter II 1 Energy Eigenvalues of an Asymmetric Rotor 9 Chapter I H 1 Standard Sources for Energy Calibration 19 2 Secondary Energy Standards of *^Dy 19 3 Efficiency Calibration Standards 22 4 Peaks Observed in Y-Spectra 36 5 The 238 and 242 kev Background Transitions 40 6 Energies and Intensities of "^Dy Transitions 46 Chapter IV 1 Intensities of K-Conversion Electrons 57 2 K-Conversion Coefficients & Transition Multipolarities 58 Chapter V 1 Coincidence Data from Sum Peaks 61 2 Specifications of Modular Units Used for Coincidence Measurements 64 3 Spectrum in Coincidence with the 197 kev Gate 80 4 Spectrum in Coincidence with the 215.5 kev Gate 81 5 Spectrum in Coincidence with the 966 kev Gate 81 6 Spectrum in Coincidence with the 962-966 kev Gate 82 7 Spectrum in Coincidence with the 995-1015 kev Gate 82 Chapter VI 1 Experimental E2 Branching Ratios 86 2 Experimental El Branching Ratios 87 3 Comparison with Single Particle Transition Rates 89 4 Even Parity Energy Levels 95 5 Theoretical E2 Branching Ratios 97 6 Theoretical Energies of Odd Parity States 99 L i s t of Figures v i Chapter I I I 1 Parameters of the Peak Fitting Program 17 2 Energy Calibration 20 3 Gamma-Ray Efficiency of Si(Li) Detector 23 4 ~"^ Dy Gamma Spectrum with Si(Li) Detector 24 5 Efficiency of Ge(Li) Detector 27 6 1 6 0Dy Gamma Spectrum with Ge(Li) Detector 28 7 Identification of Sum Peaks 43 8 Identification of Sum Contributions 44 Chapter IV 1 K-Conversion Peaks 50 2 K-X-Ray Coincidence Network 51 3 Low Energy K-X-Ray Coincidence Spectrum 52 4 High Energy K-X-Ray Coincidence Spectrum 54 Chapter V 1 Gamma-Gamma Coincidence Network 63 2 Output of TAC for 6 0Co 65 3 ^Co Coincidence Spectrum 67 4 The 915-1015 kev Coincidence Spectra 69 5 The 962-966 kev On-Peak Spectrum 71 6 The 966 kev On-Peak Spectrum 72 7 The 215.5 kev On-Peak Spectrum 73 8 The 197 kev On-Peak Spectrum 75 9 The 215.5 kev On-Peak Spectrum with Lead Shield 78 Chapter VI 1 The Decay Scheme of l6°Dy 84 2 Comparison with Single Particle Transition Rates 90 v i i A cknowledgement s I wish to express my gratitude to Dr. K.C. Mann f o r guidance and support throughout the course of t h i s work. I also thank the U n i v e r s i t y of B r i t i s h Columbia Nuclear Orientation Group f o r making some of t h e i r equipment a v a i l a b l e to me. This project was supported by Grants-in-Aid of Research to Dr. K.C. Mann from the National Research Council of Canada. 1 CHAPTER I INTRODUCTION All nuclei consist of "protons" and "neutrons", having charges of +e and zero respectively. Protons and neutrons are considered to form the two charge states of a "nucleon", the constituent of a l l nuclear matter. The complete description of a nucleus is a quantum-mechanical many-body problem, which because of its complexity leads to no specific solutions. To simplify this problem many models have been proposed, each successful to some degree in describing the behavior of certain nuclei. The earliest and the best known model is the "shell model", which assumes each nucleon to exist in an average central potential due to al l other nucleons, as a consequence of which each nucleon will be moving in a definite shell. The "magic numbers" (2,8,20,50,82,126), shown by experiments to be associated with high stability, were explained as the number of protons Z or neutrons N which f i l l the shells in this model. The shell model predicts successfully the energy, spin and parity of the low-lying energy levels of those odd A nuclei, A = Z+N, whose Z and N are close to the magic numbers. ^ The predictions of the shell model become inadequate as Z or N begin to deviate appreciably from the magic numbers. In this case the motion of the nucleus as a whole, for low energy excitations, becomes predominant over the individual nucleonic motion. Also some nuclear properties such as fission cannot be explained from the point of view of the motion of a single nucleon; rather i t has to be explained by the dynamics of the nucleus as a whole. The "collective model" proposed by Bohr*^ views the nucleus as a rotating and vibrating drop of nuclear matter, like a liquid drop. The equilibrium shape of the nucleus can be spherical or deformed (ellipsoidal), the deformation 2 occurringwhen there are a considerable number of nucleons outside a closed s h e l l , as for example i n the rare earth (150 5 A 5 194) or actinide (A i 226) regions. The equilibrium shape of the nucleus and the assumptions regarding the nature of the nuclear matter determine the type of the r e s u l t i n g l e v e l structure. The c o l l e c t i v e model of even-even deformed nuclei has been developed 1 2 31 extensively i n two basic ways. Bohr and Faessler ' ' J have studied the deformed nucleus as a symmetric e l l i p s o i d , allowing for symmetry preserving vibrations (g-vibrations) and asymmetric vibrations (y-vibrations). The rotational levels b u i l t on the ground state configuration, and those with one 8 or y quantum of vibrations are referred to as the ground state, 3 and y 41 bands. Band mixing was introduced by Lipas J within the context of the 5 6 71 symmetric rotor model. Davydov and co-workers ' * } have viewed the deformed nucleus as an asymmetric rotor (a t r i a x i a l e l l i p s o i d ) and l a t e r allowed for surface vibrations. The asymmetric rotor model and the symmetric model with band mixing have been successful to the same degree i n explaining the even pa r i t y states and t h e i r electromagnetic properties i n deformed nuc l e i . The odd p a r i t y states i n these nuclei have been studied as rotations and vibrations of an octupole shaped nucleus. J.P. Davidson's theory of odd 81 p a r i t y states 1 r e s u l t s i n a diagonal i n e r t i a l tensor and a band structure si m i l a r to that of the even parity states, i f an assumption regarding the 91 nuclear surface i s made (See chapter I I , page 12). M . G . Davidson 1 has noted that without t h i s assumption, the i n e r t i a l tensor w i l l not be diagonal, re s u l t i n g i n a more complicated energy le v e l structure. To test the v a l i d i t y of these theories, numerous experiments have been carried out on deformed nuc l e i . The decay 1 6 0Tb* 1 6 0Dy, both deformed nuclei of the rare earth region, has been studied extensively i n previous investigations. The p" ^ \ the conversion electron**'*^ and the gamma spectra***"*^ resulting from the population and depopulation of the excited states of 1 6 0Dy have been studied. Experiments on gamma-gamma coincidence*^and directional correlation 1**'* 9^ have also been performed. Although the decay scheme of 1 6 0Dy, and the spin and parity assignments of the energy levels seem well established, discrepancies exist as to the existence, placement and the intensity of some transitions. The 1 6 0Tb sample used in this investigation was obtained from New England Nuclear Inc. and prepared with an impurity of less than 1 % of other activities. The gamma, K-conversion electron and gamma-gamma coincidence spectra were analyzed and are reported in chapters III, IV and V respectively. The energy levels and their electromagnetic properties obtained from these data, presented in chapter VI, are compared to the predictions of the asymmetric rotor model and the theory of odd parity states as proposed by M.G. Davidson. 4 CHAPTER I I COLLECTIVE MODEL OF EVEN-EVEN DEFORMED NUCLEI The f i r s t step i n the development of the c o l l e c t i v e model i s the expansion of the nuclear surface R i n the laboratory reference frame L and a body-fixed frame B i n terms of spherical harmonics as R O,*) '- R [1 • I a Y x ( 8 , * ) ] ' (la) X , y X>1 RV,*») - R [1 • I a ' x Y x (e',*')] (lb) X,y X>1 In the above expansions the X<*0 terms have been set equal to unity since the nuclear volume i s to be constant. The X=l terms have been neglected as 9 ) they correspond to the t r i v i a l t r a n s l a t i o n of the centre of mass •*, Since the nuclear surface i s to be r e a l , We require that lX-y = C-Dy and - M ) V a -The expansion c o e f f i c i e n t s a.^ and a^ are related by a ' - [ a , DX ( 6 . ) ( 2 ) Xy *• Xv vy v i' v since V D v y ^ 6 i ^ s f o r m a u n i t a r v r o t a t i o n matrix connecting the reference 5 frames L and B through the three Eulerian angles 6^  = (8^,82,83). It can be shown that these a^ u*s are the time dependent generalized 91 coordinates of t h i s model , and for small o s c i l l a t i o n s , the k i n e t i c and the potential energies are given by V L 4 l c 4 | . I* (3a) where i s a mass parameter and c^ a restoring force constant, c^ has contributions from surface tension and coulomb repulsion, the two forces which 271 are assumed to be responsible for the surface o s c i l l a t i o n s . From here on we s h a l l r e s t r i c t ourselves to the quadrupole (X=2) case which describes the even pa r i t y states. The octupole (X=3) case for odd par i t y states i s discussed i n section 3. Dropping the X«2 subscript, equation 1 i s replaced by , 2 R (e,*) - R n[l • I a Y_ (8,<j>)] (4a) u=-2 v v 2 RV,4>*) - R [ l + I a 'Y (e',4.')] (4b) u<*-2 v M I f the body fixed frame i s chosen so that i t s axes (1,2,3) are along the 211 three p r i n c i p l e axes of the deformed body, i t can be shown that a|^=0 J. We can define a' • BCOSY and a* » — Siny (5) 0 ~l /2 6 where g and y are new variables determining the shape of the ellipsoid, g is the magnitude of deformation of the nucleus and y its deviation from axial symmetry, with the nucleus being symmetric about the 3 axes when y=0. Using equations (2) and (5) and the time derivatives of (see ref.9, p.18) in equations (3a) and (3b) we obtain for kinetic and potential energies V L - | cB 2 C6a) T L * f (0 2 • B2Y2) • \ I I «* (6b) k I k = 4BB2 Sin 2(y - ~- k) (6c) where I^'s and w^ 's are the moments of inertia and components of angular velocity respectively about the three axes (1,2,3) of the body-fixed reference frame. The first term in T*1 is the vibrational energy and the second the rotational energy. 9) It can be shown that the Hamiltonian for this system is given by • A A A J _ H = T + T • + i cB 2 (7) vib rot 2 v ' • A -^2 vib ' 2B F 3 S S 3| + B2Sin2(3Y) WSin(5Y) 9Y (7a) A n 2 c Jk T * 5- I - — * =- (7b) r 0 t 2 k 4BB2Sin2(Y - -f-k) A where J^'s are the components of total angular momentum on the three body-fixed axes (1,2,3), having the commutation relations >*• -A. A [J^J,,] = - i J 3 cyclically. 7 The Schrodinger equation is given by 2. The Asymmetric Rigid Rotor Model If we assume the nucleus to be a rigid triaxial ellipsoid, i.e. 8 and y are both non-zero constants, the Hamiltonian for the X»2 case describing the even parity states of the nucleus is given by j 2 H - I H 2 J : * *- (2.1) ' k 4B8 2Sin 2(y - '-y- k) The Schrodinger equation has the form where M is the projection of the total angular momentum J on the z axis of the laboratory frame. To solve (2.2) one needs to choose a set of basis vectors, the most convenient of which is the set of rotation matrices D ^ K C 1 ^ ) * W N I C N A R E T N E eigen vectors of a symmetric rotor ', having the following properties J D M K C V - - J ( J*1) D ^ ) * K DMKt e i 3 ^ ( 8 . ) . M D ^ ) We can expand the eigen vectors Vm as JM J ¥ J M < V = I 7 A K D M K < V K=-J 8 The only restriction on the choice of the body-fixed system is that its axes must coincide with the principal axes of the rotor. There are 24 ways of assigning such a right-handed coordinate system and 4^ should be invariant under rotations from one such system to another. For even nuclei, which experiments show to have K equal to an even integer, this leads to the requirement (for even parity levels) that A_K - ( - 1 ) J AR. The properly normalized ¥ satisfying the above conditions is given by *JM * jQ V l ^ * ^ < • C-1)X. K) (2.3) K=even Schrodinger's equation (2.2) can be solved using the Hamiltonian (2.1) and the wave functions (2.3). In solving this equation, a set of N linear equations in A^'s will result, where 1 r T . *"»*\ j? v e v T ^-N - f(J+2) for J - even § N • f(J-l) for J = odd. By requiring the N equations to be solvable, one obtains a polynomial of degree N in E j , the roots of which are the energy eigenvalues. The N N coefficients of equation (2.3) are then obtained for each e J f by solving the N remaining N-1 equations and normalizing Vj^ to unity. N The energy eifen values E J for J • 2,3,4 and 5 are given in table II - l . The only state function which corresponds to a definite value of K is the J=3 state with K=2, since the summation in equation (2.3) is over K=0 and K=2 with the K=0 term cancelling out. The other state functions are mixtures of K «» 0,2,4 ... etc. states. However i t can be shown that for y<15° only one 9 TABLE I I - l ENERGY EIGEN VALUES OF AN ASYMMETRIC ROTOR 2 l4Bg2-' Sin2(3 Y) 1 J 2 1 4 B B * Sin2(3 Y) 1 J S - O i l^vY . r - (i - ! s i . ( , T » * e i = 2 (5-3r) 5 l4Bg2 J Sin2(3 Y) 1 1 H 2 The energies of the J<=4 states, in units of are the solutions of the cubic equation 3 _ 90 £2 + 48[27+26Sin2(3Y)] _ 640£27+7Sin2(3Y)] B Q  £ " Sin2(3Y) £ SinH3 Y) Sin 1*^) 10 of the coefficients Av of equation (2.3) differs appreciably from zero and to A . a high degree of accuracy the wave functions can be approximated by only one value of K. For example, of the two states with J=2, one corresponds almost exactly to K=0 and the other to K=»2; of the three states with J=4, one corresponds to each value of K = 0,2 and 4. With K now a good quantum number, the energy levels can be divided into bands of definite K. The band with K=»0, having the spin sequence J = 0,2,4,6.. etc. is called the "ground state rotational band". The K=2 band with J « 2,3,4... etc. is called the "y-vibrational band", because in the symmetric rotor model this band is attributed to vibrations of the Y. degree of freedom. Bands of higher K, for example K = 4,6... etc., with J « K, K+l,... exist at higher excitation energies. The B-vibrational band, K=0 and J* 0,2,4..., observed in some deformed 7) nuclei at low excitation energies, can be accounted for in this model J in the same manner as in the symmetric rotor model, by allowing vibrations in the 8 degree of freedom. 3. Theory of Odd Parity States As mentioned earlier the octupole terms in the expansion of the nuclear surface describe the odd parity states. The coefficients in the expansion RV,*') - R 0 [ l • I a' Y (Q'A'H (3-D U=-3 can be defined a t • Cosct „. a • Z Cosn Cosw a' » ±£ Sxnw o xx ft« . c SJ21 cose a' - ±c Si2SL sinu, ± 2 SZ ± 3 /2 11 I t can be shown that the Hamiltonian f o r a rotating r i g i d octupole shaped nucleus i s given by*°3 22 1 = 1 1 - I 2 11 33 13 The components of the i n e r t i a l tensor, 1^, are equal to I = B c 2[Sin 2u(1.5+Cos 2o+/l5" CosaSino) 4-Cos2a>(4+2Cos2n«»^ SinnCosn) ] 1 1 3 I = B{ 2[Sin 2w(1.5+7Cos 2a-/l5 CosaSina) • Cos2a>(4+2Cos2n-2*^5 SinnCosn)] 22 3 I • B C 2[Sin 2u(8Sin 2ci+l) • 4Cos 2uSin 2n] 3 3 3 I « I « Be 2[Sinn(5/6 Sina+3/fO Coso) + 2/6 CosnCosa] j Sin2w 1 = 1 - 0 32 23 I 2 i - I ^ . 0 (3.3) In the body-fixed system, chosen to diagonalize the quadrupole i n e r t i a l tensor, the octupole i n e r t i a l tensor i s not diagonal. Since 1^ • 1^ are the only non-zero off-diagonal elements, only the 2 axis coincides with a pr i n c i p a l axis of the rotor. Using t h i s rotational symmetry i n the expansion of the wave function ¥ J M i n terms of D^ K( e^)» i t c a n 0 6 shown that 1** 3 *JM W2 } — C°MK " M-K3 C 3 ' 4 ) with the normalizing condition J I (»$ ) A 2 - 1 K-0 K 0 K 12 The assumption a^^a1 ±^>0 i n the theory of odd parity states proposed by J.P. Davidson8"' i s equivalent to setting u>=0. This diagonalizes the ine r t i a l tensor, resulting in more stringent symmetry conditions, which leads to the requirement that K i s even. The Hamiltonian of equation (3.2), when operating on Dj^, changes K by AK»0, ±1, ±2, thus allowing for even and odd values of K simultaneously. Schrodinger•s equation w i l l result i n N states of angular momentum J , where N = J + i l i l i l l If £j i s the energy of the N state of angular momentum J, then neglecting ft2 the Y~ constant where 1 £ 2 . e 1 = e 2 a 2 I 38 r - * h f ' i i « „ ) - *> 22 1 5 / I 2f v 11 33-* 1 22 22 21 C ( I H - r 3 3 ) 2 + 4 I13^ (3.5) No analytic forms can be obtained for the energies of the J=3 and J*4 states, since each involves the solution of a set of 4 linear equations in 4 A^'s. These eigen values are to be obtained by diagonalizing the determinants of these equations, using computer programs, for a given set As in the theory of the even parity states, the nucleus can be softened 13 to allow for surface v i b r a t i o n s * ^ . These vibrations, which are associated with the x, degree of freedom, are analogous to the 8 vibrations of the theory of the even parity states. Introduction of these vibrations r e s u l t s i n rotatio n a l l e v e l structures, b u i l t on states with one or more quanta of X vibrations. 4. Reduced E2 Branching Ratios : i i 9 ) The pr o b a b i l i t y per unit t me for an e l e c t r i c 2^-pole t r a n s i t i o n between states of and i s given by where Ey i s the energy of the emitted photon of angular momentum X, and B(EX, Jj- j^p i s an energy independent matrix element, c a l l e d the reduced EX tr a n s i t i o n p r o b a b i l i t y , defined as i M^,M^y where ojj^  i s the appropriate e l e c t r i c multiple operator defined i n the laboratory reference frame. i s related to the same operator i n the body-B fixed system, , by KXv *• XA yv v B 5") It can be shown that for e l e c t r i c quadrupole t r a n s i t i o n s , Q. , i s given by } A V Q B « i ze R2 a. ( 4 4 ) 2 v /5F ° v 14 where a^'s are defined by equation ( 5 ) . The operator Q^, which i s to be used in equation ( 4 . 2 ) , i s obtained by substituting ( 4 . 4 ) into ( 4 . 3 ) , and i s equal to The reduced transition probabilities, B ( E 2 ; J N - M ' N 1 ) , for a transition th til t from the N state of angular momentum J to the N state of J 1 , can be calculated using the of ( 4 . 5 ) and the state functions of ( 2 . 3 ) in equation ( 4 . 2 ) . The exact forms of these reduced transition probabilities are given i n references 5 and 6 . However i t can be shown that for Y<15°, with K being approximately a good quantum number, these expressions simplify to ( 4 . 5 ) B ( E 2 ; J K - M ' K ) « ( Q 2 / 1 6 ^ ) 5 C O S 2 Y ( 2 J 0 K | J ' K ) 2 B ( E 2 ; J K - M ' K - 2 ) » ( Q 2 / 1 6 ^ ) | ( l + 6 K 2 ) S i n 2 Y ( 2 J - 2 K | J ' K - 2 ) 2 ( 4 . 6 ) B ( E 2 ; J K - * J ' K + 2 ) = ( < ^ / 1 6^)|(l+ 6 K ( ))Sin 2 Y ( 2 J + 2 K|j ' K + 2 ) where ( A J K - - K . K . | J ' K . ) are the Clebsch-Gordon coefficients. 15 CHAPTER III GAMMA-RAY SINGLES SPECTROSCOPY The energies and the intensities of the gamma-rays emitted following the 8~ decay of 1 6 0Tb were measured with two Lithium drifted Germanium (Ge(Li)) crystals. The f i r s t detector used was a 45 cc coaxial detector with a resolution of 5.7 kev at 1332 kev, and the second a 35 cc coaxial with a resolution of 2.9 kev at 1332 kev. Although the results of measurements with the two detectors agreed well for f a i r l y intense transitions, the smaller detector, because of i t s superior resolution, facilit a t e d the identi-fication of weak transitions and the measurement of their energies and intensities to a greater accuracy. The spectra and the results presented in this thesis are those dbtained with the 35 cc detector. In order to provide a test for identification of sura peaks, three spectra were taken at D»1S, 7.5 and 0 cm, where D i s the distance from the source to the crystal chamber wall, with the detector's front surface 2 cm inside the chamber. The analyzing cir c u i t employed consisted of a TENNELEC 135 M preamplifier a TENNELEC 203 BLR amplifier with b u i l t - i n baseline restorer and a 4096 Multi-Channel Analyzer (MCA). 1. PEAK FITTING A limiting factor in the accuracy of energy and intensity measurements of a gamma-ray i s the uncertainty i n estimating the position of the peak and i t s area. Such estimates can be obtained with ease with good accuracy, without recourse to analytic functions, for peaks well defined above back-ground with no other peaks in their immediate v i c i n i t y . This i s not the case 16 i n general; peaks can overlap, f a l l on a Compton edge and so on - which then requires the f i t t i n g of the peak or peaks, with some appropriate function using a computer f i t t i n g program. The function and the f i t t i n g method used i n t h i s work have been described i n greater d e t a i l elsewhere 2 6**. In short, the shape of a peak may be approximated by a distorted Gaussian function, superimposed upon a step function. The function used i n the f i t t i n g routine was where y(x) = ?x * ?2x * S • E1 + E 2 (3.1) S • PjO^ - Arctan (2.0(x-P g))) (x-P ) 2 E. » P. exp — — 6 E, » P 7 exp ( x - P 8 ) 2 '2 7 * * 2 P 9 In t h i s function, Pj through P g are the f i t t i n g parameters, p j + p 2 x Providing a l i n e a r background and S the step function. E 1 i s the main Gaussian of height P^, position Pg, and standard deviation P &; i s the s a t e l l i t e Gaussian which accounts for the d i s t o r t i o n i n the pure Gaussian shape. Each spectrum was f i t t e d i n two steps i n order to reduce the number of parameters, thereby f a c i l i t a t i n g the f i t t i n g procedure i n the case of overlapping peaks. F i r s t a number of well defined peaks were f i t t e d over the whole of the energy range, relations Py/P^» pq/ pg a n <* P5~Pg w e r e obtained as functions of energy, thus reducing the number of parameters to s i x . Figure I I I - l shows the above mentioned functions obtained for the spectrum at D=>7.5 cm. As the Figure I I I - l Parameters of the Peak F i t t i n g Program 17 18 second step these functions were employed i n the o r i g i n a l function, equation (3.1), to f i t a l l the peaks i n the spectrum. The position of a peak was taken to be the position of the centroid of the main Gaussian, and i t s area as the sura of the areas of the main and the s a t e l l i t e Gaussians. The errors i n position and areas used were those returned by the RLQF (Restricted-Least-Square F i t ) subroutine of the UBC Computer Centre Library. 2. ENERGY CALIBRATION The energy c a l i b r a t i o n of the gamma spectra was done i n two steps. F i r s t a spectrum was taken of the 1 6 0 T b source and a set of standard sources l i s t e d i n Table I I I - l . The peaks of the standard sources and a l l the intense peaks of 1 6 0Tb, l i s t e d i n Table I I I - 2 , were f i t t e d using the previously mentioned f i t t i n g program and t h e i r positions found. A function of the form ENERGY • a+b(CHANN.NO.) • c(CHANN.NO.)2 was least-square-fitted to the positions and the energies of the standard 1 fi 0 peaks. The energies of the intense peaks of Tb, the secondary standards, were found from the above function. Figure III-2 shows the plot of the energies of the standard peaks against t h e i r position and the f i t t e d function with a • -74.0+.2 , b » .42541.0001 , c - -.228xl0" 6. As the second step i n the energy c a l i b r a t i o n , the energies of the secondary standard peaks of 1 6 0Tb were used i n each subsequent spectrum to obtain the energies of a l l other gamma-ray peaks. TABLE I I I - l STANDARD SOURCES FOR ENERGY CALIBRATION SOURCE ENERGY (kev) 57Co 121.97±.03 136.33+.03 2 2 N a 511.0061.002 1274.551.04 137CS 661.641.08 5*»Mn 834.811.03 6 0Co 1173.231.04 1332.491.05 TABLE III-2 SECONDARY ENERGY STANDARDS OF 1 6 0Dy ENERGY (kev) 86.8 196.9 215.5 298.4 879.3 1178.2 1272.0 21 3. EFFICIENCY CALIBRATION The t o t a l e f f i c i e n c y of a detector, defined as the r a t i o of the measured gamma-ray i n t e n s i t y I to the t o t a l i n t e n s i t y I Q , i s given by f - h <™ o where ft i s the s o l i d angle subtended by the detector and e i s the i n t r i n s i c e f f i c i e n c y of the detector, a function primarily of gamma-ray energy E. The e f f i c i e n c y of a GE(Li) detector, I/I Q> has a maximum i n the v i c i n i t y of 100 kev. For higher gamma-ray energies (E>100 kev), the function y-o decreases slowly with increasing energy, while for E<100 kev the e f f i c i e n c y drops sharply. This drop i n e f f i c i e n c y i s due to absorption effects i n the detector window which i s the insensitive layer at the front face of the detector 2** 3. To obtain the e f f i c i e n c y of the GE(Li) detector below t h i s maximum, we have used as secondary standards some of the intense t r a n s i t i o n s i n 1 6 0Dy decay i n a manner to be discussed l a t e r . Table III.3 l i s t s the standard sources available for the ef f i c i e n c y c a l i b r a t i o n of the 35 cc GE(Li) detector. These sources, encapsulated i n aluminum disks, were obtained from the International Atomic Energy Agency, Vienna. In order to obtain the r e l a t i v e i n t e n s i t i e s of the tra n s i t i o n s below 100 kev, i . e . the 86.8, 93.9 and 97.7 kev gamma-rays, a previously calibrated 3 mm Lithium d r i f t e d S i l i c o n ( S i ( L i ) ) detector was used to obtain the r a t i o of the in t e n s i t y of the 86.8 kev t r a n s i t i o n to that of the 298.3 kev I Q t r a n s i t i o n of 1 6 0Tb. Figure III-3 shows the inverse e f f i c i e n c y function, j-, of the S i ( L i ) detector for gamma-rays. The relevant portion of the l 6 0 T b gamma spectrum obtained with t h i s S i ( L i ) detector i s shown i n Figure III-4. 22 TABLE III-3 EFFICIENCY CALIBRATION STANDARDS Source Transition energy (kev) Half-Life Strength (p curies) at Jan.l, 1970 Relative Intensity (%) 57Co 122 271.6±.5 days 11.431.7% 85.011.7 136 11.411.3 1 1 3Sn 393 115.0±.5 days 4.22x105 gamma/sec. 2 2Na 511 2.6021.005 years 9.16±1.0% 181.11.2 1275 99.951.02 1 3 7Cs 662 30.5±.3 years 10.3511.8% 85.11.4 5*Mn 835 312.6±.3 days 10.961.7% 100.0 6 0Co 1173 5.28±.01 years 10.571.6% 99.871.05 1332 99.9991.001 F i g u r e I I I - 4 2 4 160 Dy Gamma S p e c t r u m W i t h S i ( L i ) D e t e c t o r C H A N N . NO. 25 A 1 ram thick aluminum absorber was placed between the source and the detector to eliminate the low energy electrons. The result of the measurement was I (298.3) IQ(86.8) 1 , w The efficiency of the GE(Li) detector was obtained at E <= 86.8 kev, using the measured intensity of the 86.8 kev transition, 1(86.8), and its total intensity, IQ(86.8), obtained from IQ(298.3) using the above ratio. The total intensities of the 93.9 and the 97.7 kev transitions were obtained from their measured intensities, by taking the efficiency of the detector at these energies to be approximately equal to the efficiency at 86.8 kev. The uncertainty in the efficiency of the GE(Li) detector at each calibration energy is due to the following factors: i) The uncertainty in calculating I due to the errors in data used; i.e. half lives, i n i t i a l source strength and systematics of decay schemes (see table III-3); ii ) The error associated with the calculation of the area under each peak, because of background estimation and random counting error; i i i ) The error from the analyzer dead time correction. Once the MCA has received a pulse for analysis, its input is blocked to a l l other pulses until the original pulse has been analyzed. A fraction of a l l pulses are lost due to this dead time, the time that the MCA input is blocked, and this fraction is the same for a l l channels since the pulses arrive at the MCA at random2*^. This correction factor was measured by analyzing on the same spectrum the signals from the source and the pulses from a pulser, generating 60 pulses per second. The pulses, fed into the preamplifier stage, are random with respect to the true signals from the source, so they have the same probability 26 of being blocked as other signals. Then the correction factor is given by the ratio of the number of pulser signals generated to the number detected, the error arising from the uncertainty in calculating the area of the pulser peak. I The inverse efficiency function, j~, of the 35 cc GE(Li) detector for gamma-ray energies in the range 100-1400 kev is shown in Figure II1-5; also I shown by the error bars at each calibration energy are the errors in j— calculated from the above factors. The curve shown is the function ~ • a + b(E-120.) + c(E-120)2 + d(E-120.)3 which was least square-fitted to the data. E is the energy in kev, and a = 485±30 c - 1.65xl0-3 b = 3.346+.03 d • - 0.8xl0 - 6 The above calibration function was obtained with the source at D=15 cm. The efficiency of the detector was also calibrated for D=0 cm, and i t was found that the efficiency calibration functions at these two distances differed, within the error limits, by a constant factor, which is the change in the solid angle. Since we are interested only in the relative gamma-ray intensities, the calibration function for D=15 cm was used for a l l three spectra with D <• 15, 7.5 and 0 cm. 4. 1 6 0Tb GAMMA SPECTRA As mentioned earlier, three gamma spectra were taken at D = 15, 7.5 and 0 cm. Figure III-6 (a through h) shows the spectrum taken at D » 7.5 cm. The positions and the area of the peaks were found using the fitting routine described earlier, and the energies and intensities found using the calibration functions. Table III-4 lists the average energies of a l l the 1 0 0 5 0 0 1 0 0 0 1 5 0 0 ENERGY ( KEV ) 1 0 U I < o (/) 3 o o 1 0 I 2 1 5 . 5 2 3 0 . 4 6 0 0 7 0 0 8 0 0 CHANN. NO. N 2 9 8 . 4 3 0 9 . 3 3 3 7 . 0 3 2 0 . 5 3 5 0 . 3 351-6 " 9 u f J 1 0 0 0 2 x 1 0 5 + , 3 9 2 . 1 1 0 5 f 3 8 6 . 8 < x o CO r— z ZD O O 3 7 9 - 5 , 4 3 2 . 6 4 8 5 . 8 1 496.6 5 1 1 . 0 2 x 1 0 1100 1 2 0 0 1 3 0 0 C H A N N . N O -1 4 0 0 1 5 0 0 2x105| 235A 105 + < C J \ LO 3 O O 2 x 1 0 ^ + 8 3 5 . 2 2 1 0 0 2 2 0 0 2 3 0 0 C H A N N . N O . 2 4 0 0 2 5 0 0 cm (D H H M I ON r o 2 x 1 0 3 | 3 1 0 0 3 2 0 0 : 3 3 0 0 3S0O 3 5 0 0 C H A N N . NO. 3600 ~~~ 3700 3800 "3900 0000 C H A N N . NO. TABLE I I 1 - 4 PEAKS OBSERVED IN y-SPECTRA 36 INTENSITY D = 15 cm 15.2 .07 .007 .01 .006 6.25 4 . 7 0 .09 .066 .02 .004 2 9 . 5 .96 .008 .39 .024 .10 (.8) ( .02) ( .003) ( .005) ( -35) ( .30) ( .01) ( .016) ( -01) .007 ( .005) (1.5) ( -09) ( .03) ( .003) ( .01) 1.44 ( .08) D = 7 .5 cm 15.5 .06 .01 .027 .007 6.45 4 . 9 0 .094 .017 .003 .022 .014 .013 3 0 . 0 .97 .008 .38 .009 .014 .036 .02 .024 1.44 (1.4) ( .001) ( .01) .006 ( .003) ( .35) ( .30) ( .01) ( .004) ( .005) ( .005) ( .004) ( .004) (1 .6) ( .10) ( .004) ( .02) ( .006) ( .008) ( .01) ( .008) ( .006) ( .08) D = 0 O i l 15.1 (1 .4 ) .10 ( .03) .07 ( .01) .005 ( .002) .007 ( .003) 6 .26 4 .78 ; .077 .06 .080 .058 .046 .29 29.2 .72 .005 .35 .15 .071 .016 .04 .71 1.37 ( .33) ( .30) ( .008) ( .003) ( .004) ( .013) ( .018) ( .02) (1 .7 ) ( .20) ( .002) ( .03) ( .02) ( .003) ( .003) ( .008) ( .03) ( .07) 37 TABLE II1-4 (continued) INTENSITY (kev) D - 15 cm D = 7. 5 an D = 0 cm 412.3 .16 (.02) S 432.5 .025 (.01) .02 (.006) .019 (.01) 478.6 .029 (.007) s 485.8 .081 (.016) .077 (.013) .083 (.014) 494.8 .067 (.011) S 496.6 .082 (.014) .027 (.009) B 505.6 .030 (.009) S 569.4 .20 (.02) .062 (.008) B 582.7 .071 (.017) .034 (.02) B 596.6 .024 (.01) R.S. 609.1 .16 (.01) .057 (.01) B 682.1 .58 (.03) .58 (.025) .47 (.03) 765.1 2.12 (•07) 2.09 (-07) 1.67 (.06) 835.2 .073 (.022) .025 (.012) B 851.8 .095 (.02) S 871.9 .08 (.02) .06 (.02) 879.3 =30.0 =30.0 =30.0 916.8 .052 (.001) S 925.0 .214 (.005) S 931.4 .096 (.014) S 962.4 10.2 (.45) 10.18 (.41) 10.70 (.41) 966.2 25.2 (.8) 25.0 (.8) 27.6 (.3) +S.C. 980.2 .11 (.01) s 1002.9 1.04 (.04) 1.04 (.03) .94 (.02) 1007.9 .082 (.006) s 1014.0 .041 (.009) s 1049.4 .39 (.03) S 1064.0 .22 (.016) .06 (.01) B 1069.1 .095 (.015) .095 (.013) .128 (.015) 1089.3 .055 (.015) s 1102.8 .57 (.02) .57 (.02) .50 (.02) 38 TABLE III-4 (continued) ENERGY INTENSITY COMMENT (kev) D = 15 cm D = 7.5 cm D = 0 cm US. 3 1.55 (.05) 1.52 (-05) 1.37 (.04) 1120.4 .105 (.003) .031 (.001) B 1173.5 2.24 (.16) 1.0 (.10) .12 - (.03) B 1178.2 14.85 (.45) 14.82 (.44) 18.00 (.45) +S.C. 1189.5 .012 (.006) S 1200.1 2.34 (.08) 2.33 (.08) 2.67 (.08) S.C. 1224.1 .19 (.01) S 1230.3 .93 (.01) S 1238.2 .038 (.008) .011 (.003) B 1251.5 .10 (.008) .10 (.01) .09 (.006) 1264.8 .024 (.008) .07 (.02) 1.90 (.10) S 1272.0 7.35 (.22) 7.37 (.23) 7.92 (.23) 1286.0 .011 (.003) .017 (.003) .106 (.009) +S.C. 1299.6 .004 .004 (.002) .09 (.01) +S.C. 1312.4 2.78 (.09) 2.78 (.09) 3.18 (.08) +S.C. 1317.8 .013 (.003) .106 (.008) S 1324.1 .046 (.001) S 1332.7 2.46 (.08) .90 (.03) .07 (.01) B 1359.1 .016 (.004) .36 (.02) S B = Background Peak S = Sum Peak R.S. «* Random Sura Peak +S.C. = Plus Sum Contribution 39 peaks observed r a the three s p e c t r a and the r e l a t i v e i n t e n s i t i e s i n each spectrum, a l l normalized to I q(879.3) = 30.00. This n o r m a l i z a t i o n i s p a r t i c u l a r l y u s e f u l as i t r e p r e s e n t s the number of gamma-rays emitted i n 100 1 6 0 T b d i s i n t e g r a t i o n s 1 2 ^ , A search f o r s i n g l e and double escape peaks o f the gamma-rays o f energies above 1022 kev re v e a l e d no such peaks i n our s p e c t r a . To i d e n t i f y the gamma-rays due to other p o s s i b l e r a d i o a c t i v e sources i n the surroundings, the 1 6 0 T b source was removed and a spectrum taken. The t r a n s i t i o n found i n the background are i d e n t i f i e d i n Table I I I - 4 . 14") Ludington et a l . ' reported two gamma-rays o f energies 237.6 and 242.5 kev; these same t r a n s i t i o n s were re p o r t e d by McAdams and O t t e s o n 1 ^ as 237.8 and 243.0 kev r e s p e c t i v e l y . In t h i s work two peaks were observed at energies o f 238.7 and 242.0 kev but were i d e n t i f i e d as the 238.6 kev gamma r a y o f 228xh and the 241.9 kev t r a n s i t i o n s from 2 2 6 R a . The i d e n t i f i c a t i o n was made on the f o l l o w i n g b a s i s . Having found these t r a n s i t i o n s i n the background spectrum, t h e i r expected areas i n the D = 15 and 7.5 cm sp e c t r a were c a l c u l a t e d u s i n g the other background peaks and compared to the observed i n t e n s i t i e s . The r e s u l t s of t h i s comparison are presented i n Table I I I - 5 . 5. SUM PEAKS Sum peaks i n general can be d i v i d e d i n t o two c l a s s e s ; those which are due to the random summing o f two t r a n s i t i o n s and those which are caused by the summing of two c o i n c i d e n t gamma-rays. The r a t e o f random summing, 1-^+2' °^ t w o t r a n s i t i ° n s Ej_ a n c* e a c ^ °^ a counting r a t e 1^ and I , i n producing a peak at an energy o f E ^ - 1 ^ ^ s g i - v e n D v : h+2 = 2 t hl2 ' ^ where T i s t h e maximum time d i f f e r e n c e between two pulses i n which they may TABLE III-S THE 238 AND 242 KEV BACKGROUND TRANSITIONS Spectrum Observed Energy Calculated Intensity from Background Spectrum Measured Intensity D=7.5 238.7 (1.7±.2)xl04 (1.5±.2)xl04 242.0 (5.2±1.3)xl03 (3.7±l.l)xl03 D=15 238.8 (2.05±.04)xl04 (2.1±.l)xl04 241.6 (6.2±.8)xl03 (5.6±l.l)xl03 41 s t i l l add together to produce one pulse of energy E j + E 2 * This time difference x depends only on the analyzing c i r c u i t employed and can be found by measuring the rate of summing of an intense gamma-ray with i t s e l f . The 596.0 kev peak i n the D=0 cm spectrum, caused by the summing of the 298.3 kev t r a n s i t i o n with i t s e l f , was used to calculate T. The count rates are I(298.3) C C9-2±.04) x 10 3 sec" 1 1 ( 5 9 6. 0) * ^ 4 3 ± ' 1 3 s e c _ 1 which res u l t s i n x = 250 nsec. Using t h i s value of T, the area of the sum peak 4 of the 86.8 kev t r a n s i t i o n with i t s e l f was calculated to be (1.3±.4)xl0 which 4 agrees reasonably well with the value of (,9±.3)xl0 for the area of the 173.0 kev peak i n the D=0 cm spectrum. The rate of coincidence summing of two cascading t r a n s i t i o n s , 1 and 2, with t r a n s i t i o n 1 preceding t r a n s i t i o n 2, i s given by I 1 + 2 - K 2 (3.4) where a s before, i s the t o t a l e f f i c i e n c y of the detector for t r a n s i t i o n 2 and K 2 i s some constant, dependent on the d e t a i l s of the decay scheme (see Chapter V, page 59). In general a peak at an energy of E j * ^ c a n r e P r e s e n t the gamma-ray corresponding to a true cross-over t r a n s i t i o n , the pure summing of the coincident gamma-rays Ej and with no cross-over t r a n s i t i o n or the r e s u l t of a certain combination of these two processes. The area of each peak has to be corrected for the possible contribution from random summing. In most cases t h i s correction was found to be too small and was neglected. The method used to ascertain the nature of a coincident sum peak i s as follows. When the distance between the source and the detector i s decreased, to the intensity of a true gamma-ray peak increases by a factor of D l 2 (—) (the ratio of the two solid angles). The intensity of a sum peak, random 2 D l 4 or coincident, increases byfcr-) , as can be seen from equations (3.3) and 2 (3.4). Since in a l l spectra the intensities of a l l peaks are normalized to the same value for the 879.3 kev gamma-ray, i.e. IQ(879.3) • 30.0, then the normalized intensities of the true transitions should remain constant when D l 2 changing the distance D, while the intensity of a sum peak increases by (~) . 2 If 1^ , I2 and I^+2 a r e t* v e intensities of the peaks at energies Ej, and Ex*%2 respectively, then a plot of Al+2 ll*2 against source-to-detector distance determines the nature of the peak at E^+E2» If the plot is a straight line with zero slope then the peak at E j + E 2 is entirely due to a true cross-over transition; a straight line with a positive slope indicates a pure coincidence sum peak. A curve would indicate a mixture of the two, in which case the value of 1^2 * n t* i e s P e c t r u m taken at the largest source to detector distance is taken as the intensity of the true cross-over transition. The sum peaks and the true transitions with large sum contributions are identified in Table III-4. The pure sum nature of the 283.3, 1264.7 and the 1359.1 kev peaks are evident in the above mentioned plots presented in Figure III-7. Figure III-8 shows the substantial sum contributions to the true gamma-rays of energies 1200 and 1286 kev. The case of the 97.7 kev peak is of interest since i t could conceivably be due to the coincidence summing of the Ko and the x-rays. If this peak Figure III-7 I d e n t i f i c a t i o n of Sum Peaks 5 1 0 1 5 S O U R C E - T O - D E T E C T O R D I S T . ( C M ) Figure III-8 Identification of Sum Contributions 1 2 0 4 5. 1 0 . 15. S O U R C E - T O - D E T E C T O R D I S T . ( C M ) 45 was a pure sum peak then I ( 9 7 . 7 ) ) ^ n D ° 0 ^ / I ( 9 7 . 7 ) |  I ( 9 3 . 9 y D » 0 \ n Da7.9 / N 1 ^ ^ / D=7.5 where the ratio of the solid angles i s known to be 35=9 2 2 . 6 "D=7.5 But i t i s observed that (h^A m ,18 and (ISSlA - !.0 V (93.9y D»7.5 \ ( 9 3 . 9 X D»0 which indicates that a part of the 97.7 kev peak i s due to a true transition. Table I I I - 6 l i s t s the energies and the adopted intensities of a l l the true transitions observed, included for comparison are the results of Gunther 131 171 et a l . J and McAdams and Otteson J . 46 TABLE III-6 ENERGIES AND INTENSITIES OP THE 1 6 0Dy TRANSITIONS Present Work ENERGIES Of Ref.17 Of Ref.13 Present Work INTENSITIES Of Ref.17 Of Ref.13 86.8 (.2) 86.8 86.7 15.3 (.8) 13.0 13.5 93.9 (.2) 93.9 - .06 (.02) .054 -97.7 (.3) - - .008 (.004) - -111.8 (.5) - - .025 (.015) - -148.5 (.3) - - .008 (.004) - -176.3 (.5) 176.4 - .007 (.003) - -196.9 (.2) 197.0 197.0 6.3 (.3) 5.2 5.3 215.5 C2) 215.6 215.6 4.8 (.3) 4.0 4.55 230.4 (.2) 230.6 230.7 .09 (.01) .082 .136 246.5 (.3) 246.4 .015 (.005) .026 -298.4 (.2) 298.6 2S8.5 29.7 (.6) 27.3 29.8 309.3 (.2) 309.6 309.6 .96 (.09) .92 .97 320.5 (.3) - 320.4 .008 (.004) - <.018 337.0 (.2) 337.3 337.1 .38 (.02) .36 .40 349.3 (.2) 349.7 349.6 .019 (.008) .018 <.014 379.5 (.3) 379.3 - .03 (.008) .017 -392.1 (.2) 392.5 392.4 1.44 (.08) 1.40 1.52 432.5 (.2) 432.7 432.6 .022 (.006) .024 .017 485.8 (.2) 485.9 485.7 .08 (.01) .088 .091 682.1 (.2) 682.3 682.2 .58 (-03) .617 .665 765.1 (.2) 765.3 765.3 2.10 ( .Ot) 2.16 2.25 871.9 (.3) 872.0 - .19 (.02) .207 -8/9.3 (.2) 879.4 879.2 530.00 530.00 530.00 962.4 (.2) 962.4 962.1 10.2 (.4) 9.42 10.2 966.2 (.2) 966.2 965.8 25.1 (.8) 24.8 25.9 1002.9 (.2) 1002.9 1002.7 1.04 G05B 1.02: 1.13 1069.1 (.2) 1069.1 - .095 (.015) .104 -1102.8 (.2) 1102.6 1102.2 .57 (.02) .56 .59 1115.3 ( . 2 ) 1115.1 1115.0 1.53 (.05) 1.48 1.58 47 TABLE III-6 (Continued) ENERGIES INTENSITIES Present Work Of Ref.17 Of Ref.13 Present Work Of Ref.17 Of Ref.13 1178.2 (.2) 1178.0 1177.7 14.8 (.4) 15.0 15.9 1200.1 (.2) 1199.9 1199.8 2.34 (.08) 2.37 2.53 1251.5 (.3) 1251.3 1250.8 .10 (.01) .104 .12 1272.0 (.2) 1271.9 1271.5 7.4 (.2) 7.48 7.9 1285.4 (.3) 1285.6 - .014 (.003) .015 -1299.6 (.3) 1299.3 1299.2 .004 (.001) .006 <.04S 1312.4 (.2) 1312.1 1311.8 2.78 (.09) 2.87 3.02 48 CHAPTER IV K-CONVERSION ELECTRONS Internal Conversion is the process by which a nucleus in an excited state loses its energy by ejecting an atomic electron from the atom, a process which is always in competition with direct photon emission. The electron shall,have a kinetic energy of E -E D > where E_ is the binding energy of the Y D O atomic electron. This process is due to the direct interaction of the bound electron with the multipole field which would have caused the emission of a gamma-ray of energy B^ . The electron may be ejected from any of the atomic shells K,L,M,... etc., following which the atom is de-excited by emitting the binding energy as an x-ray or an Auger electron. W e The Coefficient of Internal Conversion (ICC) is defined as a = ^—, where Vly and Wg are the transition probabilities for emission of a photon and of an electron respectively. The ICC can be defined for single shells as a^, a^... etc. where W „ W . eK eL ... a R " ^ — , c*L " ^ — , ... with a = a K + a L • • Y Y WeK' WeL' e t c ' a r e P r 0 D a b i l i t i e s for emission of an electron from the atomic shells K,L,... etc. Coefficients a^, a^,... etc. depend on the atomic number Z, the transition energy E^, the parity and the multipole order of the transition, but not on the nuclear wavefunctions for these enter into W^ , W^... etc. in 22) the same manner as into W , and thus cancel J. The theoretical conversion :' Y coefficients, which are used in Table IV-2, have been calculated by Sliv and 25) Band ' for and o^. Once the intensity of K-conversion electrons, 1^ , and that of the gamma-49 rays, I , have been calculated for a given transition, the experimental ICC can Y h be calculated by a K = j—• Upon comparing this value to the theoretical Y predictions, the transition multipolarity can often be deduced. 1 . K-CONVERSION ELECTRONS IN COINCIDENCE WITH K-X-RAYS A single spectrum of the conversion electrons taken with a Si (Li) detector is frequently not very helpful for measuring the intensities of the K-conversion electrons, because the peaks are too weak. This is because such a spectrum contains a very large background due to the B~ transitions and the electrons from the Compton scattered gamma-rays. There is also the possibility that a K-conversion peak may be superimposed on the L- or M- conversion peak of another transition. This background can be reduced by accepting only those events which are in coincidence with the K-x-rays, which are generated and are in coincidence with the K-conversion electrons. Other events, such as some (3 , gamma and L- or M- conversion transitions, may also be in coincidence with the K-x-rays, but the K-conversion peaks are enhanced above a l l others. Figure IV-1 shows this enhancement of the K-conversion peaks in the coincidence spectrum as compared to the singles electron spectrum. Because of different amplifier gains, the position of peaks in these spectra are different. The fast coincidence network employed is shown in Figure IV-2; the electronic equipment used were the same as those described in Table V-2. A 2 mm Si(Li) detector was used to gate the K-x-rays, and a 3 mm Si(Li) detector (with constant electron efficiency) was used as the analog detector. Figure IV-3 (a,b) shows the low energy electron spectrum obtained, and the high energy spectrum i s shown in Figure IV-4(a,b). The measured intensities of the K-conversion peaks were normalized to the F i g u r e TV -1 K-Conversion Peaks 50 C O U N T S Figure IV-2 K-X-Ray Coincidence Network 51 3 mm 5 mm T.F A . CF. T.D. Source Start H T.A.C. Stop T.S.C.A. 2 M.C.A. Gate i Delay Figure IV-3 (a) Low Energy K - X - R a y Coincidence Spectrum 52 ' N N V H O / s l N f l O O 10' 1 0 3 T -< o LO Z) O O 1 0 ' K ( 1 9 6 . 9 ) _L( 1 9 6 . 9 ) 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 C H A N N . NO. 10 5 10" I i(T + < o \ LO ZD O CJ ItV K ( 196.9 ) K ( 215.5 ) 196.9) K( 298.4 ) K(309.3 ) K ( 392.1 ) K( 765.1 ) K ( 682.1 ) w TO cr En CD era !->• era £ I CD X 1 R ) 1 O o P i H- V ^ t3 O H-D. CD O CD CO "O CD O 100 200 300 600 500 CHANN. NO. 1 0 3 K( 879.3) L( 879.3) 10' 10 * • K ( 9 6 2 . 4 ) + K ( 9 6 6 . 2 )  K ( 1002.9 ) • • • L ( 966.2 ) I t K(1102.°J) 115.3 ) * * * 1<_ * • • • • # * i • • • ••• • • * « • • ! • • * 1 K(1178.2) K ( 1272.0 ) T K ( 1200.1 ) K(1312.4 ) Jl < x o 3 O o 0 600 700 800 C H A N N . NO. 900 1000 56 gamma i n t e n s i t i e s , by assuming the 196.9 t r a n s i t i o n to be of pure E2 multi p o l a r i t y . These normalized K-conversion Intensities are presented i n 12) Table IV-1 along with the data of Ewan et a l . for comparison. The r a t i o I K(962) — v « > ^ v a '403 of Ewan et a l . was used to separate the K-conversion double I K(966) peak of the 962-966 transitions with I K(962) + I R(966) » .107 ± .002 The normalized K-conversion i n t e n s i t i e s , along with the gamma i n t e n s i t i e s were used to calculate the « K's, and to assign the m u l t i p o l a r i t i e s of the tra n s i t i o n s . These data and the adopted m u l t i p o l a r i t i e s are presented i n Table IV-2. The upper l i m i t s placed on the K-conversion i n t e n s i t i e s ' o f the 379.5, 485.8 and 1251.5 kev t r a n s i t i o n s , r e s u l t i n an E l or an E3 assignment for these t r a n s i t i o n s . The change of pa r i t y involved i n these t r a n s i t i o n s excludes the E2 or Ml p o s s i b i l i t i e s . These transitions are most l i k e l y E l , since no other E3 tra n s i t i o n s are observed and also an E l assignment being the lowest mu l t i p o l a r i t y possible, i s more l i k e l y . TABLE IV-1 INTENSITY OF K-CONVERSION ELECTRONS1" TRANSITION ENERGY (kev) K-CONVERSION INTENSITY This Work Ewan et a l . 1 2 3 86.8 19.9 (2.2) 24 (3) 93.9 .06 (.01) .08 (.02) 196.9 1.07 (.06) .88 (.04) 215.5 .16 (.03) .14 (.007) 230.4 .0039 (.0009) 298.3 .41 (.03) .39 (.02) 309.3 .017 (.004) .012 (.0015) 337.0 <.0045 379.5 <.003 392.1 .01 (.002) .011 (.0015) 485.8 <.003 682.1 .004 (.001 .005 (.0015) 765.0 .011 (.002) .0125 (.001) 879.3 .13 (.01) .103 (.005) 962.4 .031 (.004) .029 (.002) 966.2 .076 (.004) .072 (.004) 1002.9 .0015 (.0004) .0008 (.0002) 1103.0 <.0003 1115.3 .0012 (.0004) .0016 (.0001) 1178.2 .013 (.001) .012 (.006) 1200.1 .0026 (.0006) .0018 (.0002) 1251.5 <.0003 1272.0 .006 (.001) .0049 (.0003) 1312.4 .0024 (.0007) .0019 (.0001) Intensities normalized to events in 100 1 6 0 Tb disintegrations. 58 TABLE IV-2 K-CONVERSION COEFFICIENTS AND TRANSITION MULTIPOLARITIES TRANSITION ENERGY (kev) a K EXPERIMENTAL a K THEORETICAL El | E2 I Ml E3 ASSIGNMENT 86.8 93.9 196.9 215.5 230.4 298.3 309.3 337.0 379.5 392.1 485.8 682.1 765.0 879.3 962.4 966.2 1002.9 1103.0 1115.3 1178.2 1200.1 1251.5 1272.0 1312.4 1.23 1 . 1 0 = .166 .033 .042 .014 .017 <.012 <.l .007 <.04 .007 .0052 .0042 .003 .0029 .0013 <.0006 .0008 .0009 .001 <.003 .0008 .0008 .3) •2) .008) .01) .02) .005) .001) .03) .001) .01) .002) .0012) .0004) .0005) .0004) .0004) .0003) .0001) . 0003) .001) .0002) . 0003) .37 .30 .043 .033 .028 .014 .013 .011 .008 .0077 .0047 .0023 .0018 .0014 .0011 .0011 .0010 .0009 . 0 0 0 8 6 | .0008 .0008 .0007 .00068 .00064 1.50 1.25 .166 .12 .10 .05 .043 .035 .0255 .024 .0106 .0057 .0045 .0036 .0027 .0027 .0026 .0021 .0020 .0018 .0017 .0016 .0016 .0015 3.00 2.37 .30 .23 .19 .097 .087 .071 .050 .046 .025 .011 .0087 .0061 .0049 .0049 .0044 .0035 .0034 .0030 .0029 .0026 .0025 .0024 ,078 ,039 ,0037 E2 E2 E2 El El El El El El (E3) El El (E3) E2 E2 E2 E2 E2 El E l El El El El (E3) El El 59 CHAPTER V GAMMA-GAMMA COINCIDENCE SPECTROSCOPY Information derived from gamma-gamma coincidences i s necessary for the proper construction of the decay scheme of the daughter nucleus. Although sum peaks of the singles spectra provide a certain amount of coincidence information for strong t r a n s i t i o n s , some questions regarding the decay scheme can only be resolved by gamma-gamma coincidence measurements. 14") A 1005 kev t r a n s i t i o n reported by Ludington et a l . ' cannot be observed i n the singles spectrum, because of i t s low in t e n s i t y and i t s position on the t a i l of the f a i r l y intense 1003 kev peak. The existence of t h i s t r a n s i t i o n can only be ascertained by the coincidence method. Such measurements can also provide further information on the placement i n the decay scheme of four new tr a n s i t i o n s , namely 97.7, 111.8, 148.5 and 320.5 kev gamma-rays, observed i n the singles spectra. These tran s i t i o n s are expected to be d i f f i c u l t to observe i n the coincidence spectra, because of the extremely slow coincidence count rate. 1. COINCIDENCE DATA FROM SUM PEAKS Some information on gamma coincidences was obtained from the sum peaks of the singles spectra. The existence of a sum peak at an energy of Ej+E,,, established as not being e n t i r e l y due to random summing (See Chapter I I I , section 5), implies the coincidence of the two separate t r a n s i t i o n s , Ej and E^. The i n t e n s i t y of the sum peak of two cascading gamma tra n s i t i o n s E^ and E^ with gamma-ray 1 preceding gamma-ray 2 i n the cascade, i s given by J l + 2 * ll*Z2h2 T^- (5.1) 60 where as before fie^ i s the t o t a l e f f i c i e n c y of the detector for gamma-ray 2, and I j and I^+£ a r e t n e measured i n t e n s i t i e s of the gamma-ray 1 and of the sum peak. b 2 i s the f r a c t i o n of the decays of the intermediate excited states that go by t r a n s i t i o n 2 and * i s the p r o b a b i l i t y that t h i s t r a n s i t i o n takes 1 + a 2 place by gamma emission, rather than by internal conversion, where a i s the ICC c o e f f i c i e n t for t h i s t r a n s i t i o n (, - • i s the constant K_ of the equation 1 + a 2 2 3.4 of page 41). For example lo3 Ll+3 ^ ( l o 2 + I o 3 ^ 1 + a 3 Io3 Io5 1 I. = I .Be- (T °+T H T ° 4 L )(T75-) 1+5 1 5 I o 2 + I o 3 l o 4 + I o 5 l +« 5 where I Q ^ i s the t o t a l emitted i n t e n s i t y of t r a n s i t i o n i . In equation (5.1) we have neglected any angular correl a t i o n effects between the directions of emission of trans i t i o n s 1 and 2. For the purpose of obtaining coincidence information, true sum peaks (in contrast to random sum peaks) and true sum contributions to true cross-over t r a n s i t i o n s can be divided into two groups. i . Those which, on the basis of energy f i t , are the r e s u l t of the summing of only one possible pair of two gamma-rays Ej and E 2 < The existence of the sum peak of energy E » ^1*^2 i m p H - e s t n e coincidence of these two tra n s i t i o n s . Such sum peaks and sum contributions to cross-over t r a n s i t i o n s are presented i n Table V - l a). i i . Those sum peaks and sum contributions, which on the basis of energy f i t , can have contributions from two or more pairs of gamma-rays. These are shown i n Table V-l b). In such cases, i t i s not possible to decide which of the two or more pairs are actually i n coincidence. Equation 5.1 cannot be used for 61 TABLE V - l a) COINCIDENCE DATA FROM UNIQUE SUM PEAKS SUM PEAK SUM PEAK ENERGY + (E 2) ENERGY (Ej) + 283.5 (86.8) + (196.9) 966.2 (86.8) + (879.3) 384.8 C86.8) + (298.4) 1049.4 (86.8) + (962.4) 412.4 CI96.9) + (215.5) 108.9.3 (86.8) + (1002.9) 478.6 (86.8) + (392.1) 1189.5 (86.8) + (1102.8) 494.7 (196.9) + (298.4) 1200.1 (196.9) + (1002.9) 505:6 (196.9) + (309.3) 1286.8 (86.8) + (1200.1) 851.8 (86.8) + (765.1) b) COINCIDENCE DATA FROM POSSIBLEMULTIPLE SUMS SUM PEAK SUM PEAK ENERGY + (E 2) ENERGY (E x) + CE2) 980.2 (215..5) + (765.1) 1299.6 (196.9) + (1102.8) (298.4) + (682.1) (337.0) + (962.4) (230.4) + (1069.1) 1178.2 (298.4) + (879.3) (215.5) + (962.4) 1312.4 (196.9) + (1115.3) (432.5) + (879.3) 1264.8 (86.8) + (1178.2) (349.3) + (962.4) (298.4) + (966.2) 1359.1 (86.8) + (1272.0) 1272.0 (392.1) + (879.3) (392.1) + (966.2) (309.3) + (962.4) t h i s purpose, since the application of t h i s equation requires detailed knowledge of the decay scheme. 2. EXPERIMENTAL PROCEDURE The gamma-gamma coincidence spectra were taken using two GE(Li) detectors (45 cc and 30 c c ) , and the fast-slow coincidence network shown i n Figure V - l . Table V-2 specifies the apparatus used. The fast coincidence i s performed on the fast negative outputs of two constant f r a c t i o n timing discriminators. These outputs are used as the start and the stop pulses for a time-to-amplitude convertor TAC. The output of the TAC contains a peak which represents a l l the coincident events i n the two detectors. Figure V-2 shows the output spectrum of the TAC taken with a 6 0Co source i n coincidence with the 1173 kev t r a n s i t i o n . The slow coincidence i s performed by coincidence unit on the logi c pulses from two timing single channel analyzers TSCA. The TSCA #1 i s used to energy gate the desired t r a n s i t i o n fr~m the 45 cc detector (the gate detector) and the TSCA #2 i s set to gate the time peak of the TAC output. The output of the coincidence unit i s used to gate the spectrum of the 30 cc detector (the analog detector) at the input of the multi-channel analyzer. The re s u l t i n g spectrum contains that portion of the spectrum of the analog detector which i s i n coincidence with the gated t r a n s i t i o n . This spectrum w i l l also have contributions from the following sources. In the "on-peak" spectrum, i . e . with the TSCA #1 gating the desired t r a n s i t i o n , there w i l l also be events which are i n coincidence with the background under the gated peak. This can be corrected for by taking an "off-peak" spectrum, where the TSCA #1 i s moved to a nearby region of the spectrum, clear of other peaks. In applying t h i s correction, the off-peak F i g u r e V - l 63 Gamma-Gamma Coincidence Network T . F A . 1 C.F.T.D.1 T.F :A.2 CF. T.D.2 Variable Delay S top Start T .A.C • T.S.C.A. T.S.C.A. 1 2 P. A . 4 Det a Det 1 P. A . t H.V. 1 Source 2 64 TABLE V-2 SPECIFICATION OF MODULAR UNITS USED FOR COINCIDENCE MEASUREMENTS Gate d e t e c t o r : Analog d e t e c t o r : T.F.A. #1 $ 2: C.F.T.D. #1: C.F.T.D. #2: Delay: T.A.C.: T.S.C.A. #1: T.S.C.A. #2: Amp. 1: Amp. 2: Coinc. U n i t : Gate § Delay Generator: MCA: a 45 cc c o a x i a l GE(Li) from Nuclear Diodes a 30 cc c o a x i a l GE(Li) from Nuclear Diodes Ortec 454 Timing F i l t e r A m p l i f i e r s Ortec 463 Const a n t - F r a c t i o n Timing D i s c r i m i n a t o r Ortec 453 Constant-Fraction Timing D i s c r i m i n a t o r C o a x i a l c a b l e Ortec 437A Time-to-Amplitude Converter Ortec 420A Timing S i n g l e Channel Analyzer C.I. Model 1435 Timing S i n g l e Channel Analyzer Tennelec 203 A c t i v e F i l t e r A m p l i f i e r Tennelec 203 BLR A c t i v e F i l t e r A m p l i f i e r w i t h B a s e l i n e Restorer Ortec 418 U n i v e r s a l Coiacidence or Nuclear Chicago 27351 Coincidence U n i t Ortec 416 Northern S c i e n t i f i c NS-900, 1024 Channels 'Figure V - 2 60, Output of TAC f o r Co t5 800 -6 0 0 -Source Gate Scale 6 0 C o 1173 Kev .68 nsec/Chanl COINCIDENCE GATE 20. nsec col 3 o o 400 6.2 nsec.FWHM 200 + 14.7 nsec.FW1/10M 50 70 90 CHANN. NO. 110 66 spectrum has to be corrected for any difference between the background intensities in the gates of the two spectra and any measurable decay of the source between the two measurements. An example of on-peak and off-peak spectra of 6^Co taken in coincidence with the 1173 kev transition i s shown in Figure V-3. The low energy portions of these spectra, below 1 Mev, are omitted. Chance coincidences are another contribution to the on-peak spectrum. The rate of these random coincidences between a gated transition i and another transition j i s given by c i j ° Vj 2 T where 1^ i s the counting rate of transition i in the gate detector and 1^  i s that of transition j in the analog detector; 2T i s the width of the gate set by TSCA #2 on the time peak (See Figure V-2). After background corrections have been made with the off-peak spectrum, the following method can be used to correct the on-peak spectrum for chance coincidences. I f a spectrum i s taken in coincidence with a transition i , then any appearance in this spectrum of transition i must be entirely due to chance coincidences. If C^ i s the intensity of this peak, then the chance contribution to any other peak j in the coincidence spectrum i s given by C i j ' i j C i i where, as before, 1^ and 1^  are the transition rates in the analog detector known from the singles spectra. In this way a l l peaks in a coincidence spectrum may be corrected for chance coincidences. 68 3- COINCIDENCE MEASUREMENTS POR 1 6 0Dy Gamma spectra were taken i n coincidence with the 197, the 215.5 and the 966 kev transitions, the 962-966 kev double peak and the approximate energy region 995-1015 kev. On-peak and off-peak spectra were taken for each of the five gates. The gated region 995-1015 kev w i l l contain i n addition to the 1003 kev transition the 1005 kev transition, i f i t exists. Figure V-4(a,b) shows the on-peak and the off-peak spectra. The portions of both spectra above 500 kev are not shown since no peaks were observed in these regions. Figure V-5 shows the spectrum in coincidence with the 962-966 kev double peak. The spectrum i n coincidence with the 966 kev transition i s shown in Figure V-6. The energy regions above 550 kev of both of these spectra are omitted, since no peaks were observed in these regions. The 962 and the 966 kev peaks were not separated by our gate detector. Thus to gate the 966 kev transition, the gate was reduced to half i t s former width (when set on the double peak) and moved to the high energy side of the double peak. The spectrum in coincidence with the 215.5 kev transition i s shown in Figure V-7(a,b). Because of low count rates, the portion of the spectrum above 1150 kev i s omitted. Figure V-8(a,b) shows the spectrum taken in coincidence with the 197 kev transition. In the course of analysis of these spectra, certain peaks occurred which did not correspond to any of the known transitions. These peaks, which were 2 to 3 times as wide as the other peaks, occurred at energies of E^E^-Eg, where E^ i s the average gate energy and E^ , i s the energy of an intense transition. In the coincidence spectra these peaks are identified as E(S), where E i s the peak energy. F i g u r e V-J+ (a) ' The 915-1015 kev Coincidence Spectra • 69. LT) CO* CNI O CO CNJ LO CXI CJ) CO cn co C D 00 < UJ J o X o < UJ CL O CNI O siNnoo 10 103 t col o o i o f c + 10' f 10 0 298.4 309.3 I 392.1 1 0 X ON -PEAK • • « « * • * « ** « • • • •« • • • • • «* • • • «• • • • • « • O F F - P E A K * * . * 200 250 300 350 C H A N N . NO. e . o Figure V - 5 "The 962-966 kev On-Peak Spectrum 71 oo cn CNJ LOj CNI CO CNJ CO co 00 CO CD CO LO 00 CNJ CD ro CO CT) O CO o] ro ro O ro CNJ CO cn o o co o o CNJ < u o o CNI o siNnoo IO4 1 9 6 - 9 . 2 9 8 . 4 1LT 2 1 5 . 5 oo t— -z. Z> O o 1 0 ' 9 3 . 9 3 0 9 . 3 3 9 2 . 1 '3 CD ro i—* PC <! o' 3 I - a co co I id CD O c + C 3 • » • • •• • • • • • CD I 1 0 ' 1 0 0 2 0 0 C H A N N . NO. 3 0 0 4 0 0 1 0 3 665(S) 75Q(S) 2 10 i to . 3 O o 10' 879.3 . 900 (S) • « 962.4 985(S) 1056(S) 1095(S) »• • • • • • • « • • «• • • 10' 0 *** * -500 600 TO 800 8 6 . 8 10 2 1 5 . 5 2 9 8 . 4 1 9 6 . 9 1 0 4-ZD O O 1 0 ' 1Q2(S? 2 3 0 . 4 . T 2 4 6 . 5 6 8 2 . 1 3 0 9 . 3 I  3 3 7 . 3 9 2 . 1 5 7 0 ( S ) H9 CD ?r CD o I CD ?r CO >U CD O c+ <S • ... • • •••* • • era < I CO 1 0 1 0 0 2 0 0 3 0 0 C H A N N . N O . 4 0 0 5 0 0 10* 1 0 2 H •v A • CO 3 o 1 0 ' 4 8 7 9 . 3 9 6 2 - 9 6 6 9 8 0 8 0 0 ( S ) 1 1 0 2 . 8 1 0 0 2 . 9 1115.3 1178.2 > • • • * • 4 • «• ** • TO CD <2 I CO « • • • # • 1 0 0 6 0 0 "7TjrJ " 8 u f J * " • . . . — ~»—* *•* * * — **— -• **** •""* i o o o CHANN. NO-ON 77 On the basis of the above observations, i t was suspected that these peaks were caused by gamma-rays scattering from one detector into the other and depositing just enough energy to trigger the gate. The process should be Compton scattering, (almost backscattering). Calculations show that with the geometry used, each of the peaks marked with an (S) can be attributed to t h i s process. To check t h i s lead shields were placed between the detectors and a spectrum taken i n coincidence with the 215.5 kev t r a n s i t i o n . This spectrum i s shown i n Figure V-9(a,b) along with a spectrum taken without the lead shields. Comparison of these two spectra confirms that these peaks are due to scattering from one detector into the other. The i n t e n s i t y of each peak i n the on-peak spectrum was corrected for background and random contributions. Tables V-3 through V-7 present the data and the corrected i n t e n s i t i e s for the f i v e gates 197, 215.5, 966, 962-966 double peak and the energy region 995-1015 kev respectively. These i n t e n s i t i e s have a l l been normalized to counts i n 5,000 seconds. The existence of the transitions 97.7 and 246.5 kev i n the spectrum taken i n coincidence with the energy region 995-1015 kev, confirms the existence of the 1005 kev t r a n s i t i o n . 1 o 2 1 1 0 ' i 1 0 ° t to 3 O o 1 0 ' 1 0 ' T 1 0 0 8 6 . 8 1 9 6 . 9 2 9 8 . 4 • • • • • • • • • 2 1 5 . 5 3 9 2 . 1 • • BARE SOURCE > • • • • • • • WITH LEAD SHIELD * * ** ** J - " *" » tt * • I I I HI t t « M I t t ttt*tt*l * *** * t I H t t t 5 0 100 CHANN. NO. 150 2 0 0 i-3 t r CD ro CD < o I •n CD ju TT CO CD O r+-c+ tr CD sa Cb CO t r CD M CK5 V O C O 1 0 2 + 1 0 ' 4 1 0 ° 4 LO o o 2 1 0 -t 1 0 ' 4 1 0 0 6 6 5 C S ) J | 7 4 9 ( S ) , • • • #• • • i if tr • i i t 7 6 5 . 1 7 9 4 ( S ) 8 7 9 . 3 *. 9 6 2 . 4 t~ 1 0 5 6 ( S ) ,901 <S.) I'.. '. f • "y 2 5 0 •n't 1*^  3 0 0 C H A N N . N O . 994(5.) 1 0 9 6 ( S ) B A R E S O U R C E W I T H L E A D S H I E L D **.«»«....«....' * 3 5 0 4 0 0 era c CD < I VO cr -v3 VO 80 TABLE V -3 SPECTRUM IN COINCIDENCE WITH THE 196.9 kev GATE ENERGY ON-PEAK INTENSITY OFF-PEAK INTENSITY CORRECTED FOR BACKGROUND CORRECTED FOR CHANCE COINCID. 86.8 3730 (30) 1430 (25) 2300 2150 148.5 14 (5) <4 >10 >10 196.9 300 (20) 260 (10) 40 215.5 770 (20) 170 (10) 600 570 230.4 44 (6) <2 >42 >37 246.5 19 (7) <2 >17 >17 298.4 620 (15) 290 (15) 230 110 309.3 63 (9) 10 (2) 53 49 337.0 22 (7) <2 >20 >18 349.3 8 (3) <1 >7 > 7 392.1 14 (6) 15 (3) 682.1 740 (20) 185 (15) 555 555 765.1 530 (20) 84 (15) 446 446 879.3 14 (3)s 15 (2) 962+966 24 (7) 21 (3) 1002.9 16 4 <1 >15 >14 1102.8 6 (1) 2 (1) 4 4 1115.3 12 (1) 1 11 9 1178.2 4 (1) 3 (1) TABLE V-4 SPECTRUM IN COINCIDENCE WITH THE 215.5 kev GATE ENERGY ON-•PEAK OFF-•PEAK CORRECTED INTENSITY INTENSITY INTENSITY 86.8 2400 (35) 1220 (50) 1180 93.9 28 (7) <10 ^ >18 196.9 770 (17) 225 (20) 545 215.5 120 (10) 150 (20) 298.4 350 (15) 340 (20) 309.3 10 (2) 9 (2) 392.1 11 (2) 13 (2) 765.1 18 (5) 6 (2) 12 879.3 14 (4) 13 (2) 962.4 150 (7) 7 (1) 143 966.2 11 (2) 12 (2) TABLE V-5 SPECTRUM IN COINCIDENCE WITH THE 966 kev GATE ENERGY ON-•PEAK OFF-PEAK CORRECTED INTENSITY INTENSITY INTENSITY 86.8 1150 (50) 1120 (50) 93.9 60 (30) <10 50 196.9 175 (25) 160 (20) 215.5 175 (25) 165 (30) 230.4 28 (8) 24 (5) 298.4 2280 (30) 270 (10) ^2000 309.3 <20 15 (3) 320.5 20 (6) <5 >15 392.1 70 (8) 11 (4) ^60 TABLE V-6 SPECTRUM IN COINCIDENCE WITH THE 962-966 kev GATE ENERGY ON-•PEAK OFF -PEAK CORRECTED INTENSITY INTENSITY INTENSITY 86.8 1860 (30) 1120 (50) 740 93. y 38 (12) <10 *v»30 196.9 180 (30) 160 (20) 215.5 720 (50) 165 (30) 550 230.4 20 (S) 24 (5) 246.5 12 (2) 11 (3) 298.4 1940 (40) 270 (10) 1670 309.3 83 (S) 15 (3) ^70 337.0 35 (7) <10 >25 392.1 40 (7) 11 (4) ~30 485.8 12 (4) 4 (2) 8 TABLE V-7 SPECTRUM IN COINCIDENCE WITH THE 995-1015 kev GATE ENERGY ON-•PEAK OFF-PEAK CORRECTED INTENSITY INTENSITY INTENSITY 86.8 490 (8) 435 (8) 55 97.7 6 CD 3 (1) 3 196.9 204 (5) 48 (3) -v.160 215.5 46 (4) 58 (4) 230.4 2 (1) 2 (1) 246.5 6 (1) <1 >5 298.4 58 (3) 55 (4) 309.3 3 CD 2 (1) 392.1 2 CD 2 (1) 83 CHAPTER VI RESULTS AND MODEL COMPARISONS The decay scheme of 1 6 0Dy, constructed on the basis of our gamma, K-conversion electron and gamma-gamma coincidence measurements, is presented in Figure VI-1. When assigning the spin values of some energy levels we have also used the results of the directional correlation measurements of references 18 and 19, and the coincidence results of reference 14 for guidance and confirmation of our results. The spin assignments are discussed in section VI-1. The decay scheme of Figure VI-1 is essentially the same as those reported by other investigators, although i t differs in some details. Specifically, transitions 237.6 and 242.5 kev reported by Ludington et a l . 1 4 ^ are found to belong respectively to the naturally occurring 2 2 8Th and 2 2 6Ra activities. The new 111.8 kev gamma-ray is placed in the decay scheme, on the basis of energy f i t , as a transition between the 1398.8 and 1286.8 kev levels. The new 97.7, 148.5 and the 320.5 kev transitions were observed in the spectra taken in coincidence with the 995-1015, the 197 and the 966 kev gates respectively. 141 The placement of the transition 1285.8 kev by Ludington et al. 1 as populating the 0 + ground state from the 3" state at 1286.8 kev, is very 171 improbable. We agree with the suggestion by McAdams and Otteson 1 that this transition takes place from an energy level at 1285.8 kev, established by 201 Grigor'ev et al. ' as a J«l state at 1285.4 kev, to the ground state. Our results showed that the energy of this peak shifted from 1285.4 kev to 1286.5 kev when D, the "Source-Detector" distance, was decreased from 15 cm to 0 cm. Since this peak is not a pure sum peak (see Figure III-S), we conclude that there is a true cross-over transition of energy 1285.4 kev, having at close distances F i g u r e V I - 1 84 co i CM T - OJ OJ n f o i i n r o <- CM ^ l l l + l l I + '—>\ ' *—' OJ + OJ OJ + 3e **** C o e ,«5c> $-t<L o °el 9 e0/ in ro to r7 I rTh CO ro lO CO CO CO CD co co to co in <r i r i c n c O L n c o c o c o a ) LO CO ro CO CM CM CM CM <~ o CO o CO CO cn OJ + o * o »-> N ro CO OJ CO CO CO The Decay Scheme of 16: Dy > o w 6 f > o cc LU z LU 85 contributions from the coincidence summing of the 1200 kev and the 86.8 kev t r a n s i t i o n s . 1. SPIN ASSIGNMENTS AND BRANCHING RATIOS The spin, J , of the positive p a r i t y levels of 160Dy have been established unambiguously by e a r l i e r investigations on the basis of E2 branching r a t i o s , d i r e c t i o n a l c o r r e l a t i o n measurements and the predictions of the c o l l e c t i v e model. Transitions between these even p a r i t y levels are a l l of E2 multi-p o l a r i t y . The experimental branching r a t i o s for two E2 t r a n s i t i o n s from the i i state J j N ^ to two f i n a l states and JfN^, a l l with po s i t i v e p a r i t y , are presented i n Table VI-1. N i s an ordinal quantum number, labeling the states of the same J i n order of increasing energy. I t w i l l be shown i n section VI-2 that K i s a reasonably good quantum number for the even p a r i t y states, so that these states may be i d e n t i f i e d with the two J and K quantum numbers instead of J and N. The odd p a r i t y states of 1 6 0 Dy depopulate mostly by E l t r a n s i t i o n s to the even pa r i t y l e v e l s . The experimental E l branching r a t i o s are presented i n Table VI-2. The choice of E l m u l t i p o l a r i t y i s made for the gamma rays 379.5, 485.8 and 1251.5 kev, neglecting the E3 p o s s i b i l i t y for reasons previously stated (See chapter IV, page 5 6 ) . Since E l tra n s i t i o n s are prohibited by the c o l l e c t i v e model, these tr a n s i t i o n s must be of single p a r t i c l e o r i g i n '. The theoretical branching r a t i o for two E l tra n s i t i o n s from the odd p a r i t y state J^K^ to two even pa r i t y states Jffif and J^K^, i s given by B(E1;J.K* J f K £ ) B(El;J iKj- J'fKf) ( J ^ K . ^ - K J J t U f K f ) (6.1) TABLE VI-1 EXPERIMENTAL E2 BRANCHING RATIOS Initial level (kev) 21 V2 B(E2;JiNi-MfNf) JiNi**JfN£ B(E2;J1Ni'M^) 966.1 966.1 1049.0 1155.8 966.2 879.3 682.1 879.3 765.1 962.4 871.9 1069.1 22 + 01 22 -*• 21 22 + 41 22 •*• 21 31 •> 41 31 -> 21 42 -> 41 42 21 , 521.03 .0681.006 .641.05 5.611.3 TABLE VI-2 EXPERIMENTAL El BRANCHING RATIOS Initial level (kev) 1264.6 1286.8 1358.4 1386.3 1398.8 1535.1 Y2 215.5 298.3 1002.9 1200.1 309.3 392.1 230.4 337.0 1115.3 1312.4 485.8 379.5 Branching Ratio .44±.05 .76±.05 1.3±.2 •74±.12 .89±.06 1.3±.4 where (J. 1K.K--K. | J. 1J JC-) are the Clobsch-Gordon coefficients. For K-forbidden 1 i t l ' 1 f t El transitions, i.e. for |K^ -K-^ j > 1, the branching ratios are calculated from the expression given in reference 23. The J and the K values of the odd parity levels were assigned by comparing the experimental El branching ratios of Table VI-2 to the predictions of equation (6.1) for a l l possible values of and K^ . These comparisons are provided in the following pages. Information on the K values of these levels were obtained by comparing the observed intensities of the transitions to the even parity levels, to the single particle transition rates as given in reference 24. Those transitions whose multipolarities were not determined by conversion electron measurements, were assigned the lowest possible electric multipolarity, which was El in a l l cases. The intensities of the transitions from each level were normalized so that the ratio of the observed intensity to the single particle estimate for the transition to the K=0 band, i.e. to the 86.8 or 283.7 kev levels, was unity. The ratio of these normalized intensities to the single particle estimates are presented in Table VI-3 and shown schematically in Figure VI-2. The broad lines and the semi-broad lines represent the transitions, whose intensities are enhanced over the normalized single particle estimates by factors of greater than 50 and between 10 and 50 respectively. The narrow lines represent the transitions which are enhanced or slowed by factors of less than 10, attributable to the statistical factors which we have neglected. K-forbidden transitions are slowed by factors which depend on the degree of forbiddehness v =» AK-1; the larger the v the more inhibited the transition 9^. The enhancement or the inhibition of the transitions to the K»2 band, as compared to those to the K=0 band, provide information on the K assignment of TABLE VI-3 COMPARISON WITH SINGLE PARTICLE TRANSITION RATES Initial Final Ratio K. Level Level r l (kev) (kev) 1264.6 86.8 0 1 966.1 2 120 >2 1049.0 2 53.3 1286.8 86.8 0 1 283.7 0 .77 1 966.1 2 .20 1358.4 86.8 0 1 966.1 2 6.7 1,2 1049.0 2 9.0 1386.3 283.8 0 1 1049.0 2 24 1155.8 2 17.6 >2 1288.6 2 20 1398.9 86.8 0 1 283.7 0 .90 966.1 2 .22 1 1049.0 2 .27 1535.1 283.7 0 1 1049.0 2 13.3 1155.8 2 11 >2 1288.6 2 18.8 ENERGY (kev) n o a 12 *i H-cn O ti co H* ti 0<S H CD *0 fu *•< «r+ H-O CD t-3 f-> C/> M-c+ M-O y r+ CD M 1 5 3 5 - 1 -1 3 9 8 . 8 -1 3 8 6 . 3 -13 5 8 . 4 1 2 8 8 . 6 1 2 8 6 . 1 2 6 4 . 6 1 1 5 5 - 8 1 0 4 9 . 0 9 6 6 - 1 2 8 3 . 7 -T T J K . - 4 2 , 3 4-3 1 4 2 , 3 2 5 2 3 2 4 3 2 1 2 2 2 2 + 4 0 H I 8 6 . 8 0 . 91 the i n i t i a l odd parity level. For example for the 1264.6 kev level, the enhancement of the transitions to the K=2 band by factors of 120 and SO over those to the K«0 band favors an assignment of 1L-2. If was equal to 0 or 1, the transitions to the K=2 band would have been retarded or unchanged respectively, relative to those to the K*0 band. The justifications for the J and the K assignments are stated below for each of the seven odd parity levels. Level 1264.6 kev J«2, K=2 The three El transitions from this level to the final even parity levels - 32, 22 and 20 restrict the spin of this level to J « 2 or 3. The theoretical branching ratios for the transitions 215.5 and 298.3 kev, i.e. B(El,JiKi-*-32') B(El' J.K.-+22)' ^ o r P o s s i , J l e values of J^K^ are 0 1 2 3 2 2.0 2.0 .50 3 8.75 8.75 1.40 .35 Comparison to single particle estimates and the experimentally observed branching ratio of .44+.05 are consistent with the assignment J^°2t K^ =»2. The J=2 assignment is in agreement with the results of directional correlation measurements of references 18 and 19. Level 1285.4 kev J°l The only transition observed from this level is the 1285.4 kev transition 20) to the ground state. Grigor'ev et al. J have identified this transition, on the basis of conversion electron measurements, to be of multipolarity El. This restricts the spin assignment of this level to J«l. 92 Level 1286.8 kev J=3, K=l Since this level depopulates by El transitions 1002.9 and 1200.1 kev to the levels JfK^ • 40 and 20 respectively, the spin of this level is restricted to J=3. The branching ratio for these two transitions, i.e. B(El;3K.-*40) B(E1;3K^20) ' f o r P o s s i b l e v a l u e s o f K i a r e K.= 0 1 2 3 3 1.33 .75 .75 .75 The observed value of .76±.05 is consistent with any of the K assignments 1, 2 or 3. The assignment K=l is more plausible since transitions from this level to the K=2 band are not enhanced over those to the K=0 band. Level 1358.4 kev J=2 The two El transitions from this level, i.e. the 309.3 and 392.1 kev transitions, populate states of JK * 32 and 22. This restricts the J assignment of this level to 2 or 3. The branching ratios for these two trans-itions for the possible values of J^K^ are 1 0 1 2 3 2 2.0 2.0 .50 3 8.75 8.75 1.40 .35 Although the observed value of 1.4±.2 suggests an assignment J^K^ = 32, this level has been identified by directional correlation measurements as a J=2 state^**^. Also the comparison with single particle estimates do not support a K*2 assignment. This level, with a J=»2 assignment, will not 93 correspond to any definite value of K, and could therefore correspond to the mixing of various K values, as suggested by Gunther et a l . 1 3 ^ . Level 1386.3 kev J»4, K>2 or 3 The depopulation of this state by two El transitions 230.4 and 337.0 kev to the states with JK «= 42 and 32, restricts the spin of this state to J»3 or The branching ratio of these two transitions for possible values of J.K. are 0 1 2 3 4 3 1.29 1.29 1.29 .143 4 5.42 5.42 .60 .60 5.42 Comparison with single particle estimates and the observed value of .74±.12 support the assignment J«4 and K»2 or 3. Level 1398.8 kev J«3, K*l Since this state depopulates by the two El transitions 1115.3 and 1312.4 kev to the final states JK= 40 and 20, the spin of this level is restructed to J«3. The branching ratio for these two transitions for possible values of K. are ^ \ K. J i ^ \ 0 1 2 3 3 1.33 .75 .75 .75 The observed value of .891.06 is consistant with any of the three assignments K i*l, 2 or 3. The K<=1 assignment is more plausible, since the transitions to the K>2 band are neither enhanced nor retarded as compared to those to the K=0 band. 94 Level 1535.1 kev J M , K»2 or 3 Since the E l tran s i t i o n s 379.5 and 485.8 kev j o i n t h i s l e v e l with the f i n a l states JK » 42 and 32, the spin of t h i s l e v e l has to be J=3 or 4. The branching r a t i o s for the possible values of J.K. are 0 1 2 3 4 3 .775 .775 .775 7.0 4 .185 .185 1.65 1.65 .185 The observed value of 1.3±.4, and the evidence from the single p a r t i c l e comparison that Kj*2, support the assignment J*»4 and K»2 or 3. 2. MODEL PITTING FOR THE POSITIVE PARITY LEVELS The theory of a r i g i d asymmetric rotor was presented i n section 2 of chapter I I . The two parameters of t h i s theory, i . e . the asymmetry parameter y -h2 S : and the energy scale factor , are best obtained using the two states of 4 B 8 2 J»2. Equating the expressions for the energies of these states, given i n Table I I - l , with the observed values of 86.8 and 966.1 kev we obtain Y - 11.9° and -2—- » 19.91 kev. 4B6 2 S i n e e y i s less than 15°, K i s es s e n t i a l l y a good quantum number. This leads to the energy levels forming into bands of K=0 wi t h J=0,2,4..., and K=2 w i t h J=2,3,4... . This value ofy i s i n excellent agreement with the y = 11.9° of ; reference 12 and y * 12.2° of reference 5. The energies of a l l other positive pa r i t y levels are calculated using these two parameters. These theoretical predictions are presented i n Table VI-4, along with the observed values. With a maximum deviation of 1.8%, the agreement TABLE VI-4 EVEN PARITY ENERGY LEVELS STATE J K OBSERVED ENERGY (kev) ASSYM. ROTOR PREDICTIONS % DEVIATIONS 2 0 86.8 £86.8 -4 0 283.7 287.3 %1.3 2 2 966.1 =966.1 -3 2 1049.0 1052.7 %.35 4 2 1155.8 1171.0 %1.3 S 2 1288.8 1313.1 %1.8 96 between theory and experiment is excellent. Another test of the theory is the comparison of the predicted E2 branching ratios with the observed values. Using the value of Y * 11.9° in equation ( 4 . 6 ) of chapter II, these theoretical predictions are calculated. These predicted branching ratios are presented in Table IV-5 along with the experimentally observed values. 3. MODEL FITTING FOR THE ODD PARITY STATES The theory of the odd parity states was presented in section 3 of chapter II. The application of the theory is facilitated by noting that the moments of inertia of equation ( 3 . 3 ) of chapter II satisfy the condition W ^ a " 1 2 B ? 2 ( 6 - 2 ) Equating the energies of the two J=2 states, i.e. 1264.6 kev and 1358.4 kev, 1 2 with e* and of equation ( 3 . 5 ) of chapter II, and using the above condition, we obtain I = 5.999 ± (35.564 - i f ) 11 13 I 3 3 = 5.999 ; (35.564 - I* ) (6.3) I = .0008 2 2 where I and I must have opposite signs appearing in front of the square * 1 33 root. It was found that the energy eigenvalues were the same for the sign combinations and -+ for I,,L . Also since I and I are real, Il | - 5.96. 11 33 11 33 1 13 The energies of the two J=l states are calculated, and they are ej * 1247.3 kev = 1275.1 kev. Using the expressions of equation (6.3), the matrix equations of the J»3 TABLE VI-5 THEORETICAL E2 BRANCHING RATIOS INITIAL STATE J i W f | OBSERVED VALUE ASSYM. ROTOR PREDICTIONS 966.1 22 -+ 00 22 -+ 20 .52±.03 .48 966.1 22 •»• 40 22 -*• 20 .068±.006 .057 1049.0 32 •+ 40 32 f 20 .64*.OS .70 1155.8 42 + 40 42 20 5.6+1.3 7.8 98 and J=4 states are expressed in terms of the one variable I . The eigenvalues of these states are obtained by diagonalizing their determinants, for various values of I 1 3 varied between the limits -5.96 and +5.96. It was observed that the eigenvalues of the J»4 state were insensitive to variations of I 1 3 , remaining constant to within .1 kev. The eigenvalues of the J=3 state, because of the asymmetry of its determinant, did not converge for a l l values of I l 3 . But whenever these eigen values converged, they converged to the same value to within .1 kev. The theoretical predictions of the energies of the J«l,2,3 and 4 states are presented in Table VI-6, along with the observed values. Since variations of I,, are found to be insignificant, I can be assigned any value consistent with equations (6.'3) and (3.3) of chapter II. 4. CONCLUSIONS The information deduced from the present experimental data, and those of the other investigations, lead to a fairly complete decay scheme of 1 6 0Dy, populated by the B" decay of 1 6 0Tb. The four new transitions found in this t investigation have very low intensities. Should there be any other transitions, as yet undetected, they must be extremely weak. Comparison of the energies of the even parity levels and the branching ratios for transitions from these levels, to the predictions of the asymmetric rotor model demonstrate the validity of this model for the 1 6 0Dy nucleus. Although the symmetric rotor model with band mixing enjoys the same degree of success in predicting these observed values, the asymmetric model is more appealing because of its simplicity in having only two parameters. A unique interpretation of the odd parity states in 1 6 0Dy, like that of the even parity states, does not seem possible at present. There is fair TABLE VI-6 THEORETICAL ENERGIES OF THE ODD PARITY LEVELS STATE J N OBSERVED ENERGIES THEORETICAL N E J % DEVIATION 1 1 1247.3 2 1 1264.6 51264.6 1 2 1285.4 1275.1 % .8 3 1 1286.8 1317.2 %2.3 2 2 1358.4 51358.4 4 1 1386.3 1372.1 %.10 3 2 1398.8 1483.5 %5.7 4 2 1535.1 1648.4 %6.2 100 agreement between the observed energies of these levels and the predictions of the theory of odd parity states as proposed by M.G. Davidson*^. However, many difficulties are encountered in applying this model even with the assumption of rigidity of the nucleus, as in solving for the eigenvalues of an asymmetric matrix. Unlike the model proposed by J.P. Davidson , which requires K to be an even integer, this model is consistent with the experimental evidence that K can have odd values. An alternative explanation would be the 13") mixing of rotational bands of K»0, 1 and 2 as proposed by Gunther et al. . It is hoped that further development of the theory of odd parity states will include predictions of El transition probabilities from these levels to the even parity states. References 101 1. A. Bohr, Dan. Mat. Fys. Medd 26 No. 14 (1952) 2. A. Faessler and W. Greiner, Z. Physlk 168 (1962) 425 3. A. Faessler and W. Greiner, Z. Physik 177 (1964) 177 4. P.O. Lipas, Nucl. Phys. A119 (1968) 398 5. A.S. Davydov and G.P. Fillipov, Nucl. Phys. 8 (1958) 237 6. A.S. Davydov and V.S. Rostovsky, Nucl. Phys. 12 (1959) 58 7. A.S. Davydov and A.A. Chaban, Nucl. Phys. 20 (I960) 499 8. J.P. Davidson, Nucl. Phys. 33 (1962) 664 9. J.P. Davidson, Collective Models of the Nucleus. Academic Press, (1968) 10. M.G. Davidson, Nucl. Phys. 69 (I965) 455 11. 0. Nathan, Nucl. Phys. 4 (1957) 125 12. G.T. Ewan et al, Nucl.Phys. 22 (1961) 610 13. C Gunther et al, Nucl. Phys. A122 (1968) 401 14-. M.A. Ludington et al, Nucl. Phys. A119 (1968) 398 15. M. Finger et al, Czech. J. Phys. Big (1969) 1017 16. G.E. Keller and E.F. Zganjan, Nucl. Phys. A147 (1970) 527 17. R.E. McAdams and O.H. Otteson, Z. Physik 250 (1972) 359 18. J.M. Jaklevic et al, Nucl. Phys. A99 (1967) 83 19. K.S. Krane and R.M. Steffen, Nucl. Phys. A164 (1971) 439 20. E.P. Grigor'ev et al, English Translation in Acad, of Sci. USSR Bull. (Phys. Ser.) 33 (1969) 585 21. K.T. Hecht, in Selected Topics in Nuclear Spectroscopy, Edited by P.J. Verhaar, North-Holland Pub. Co. (1964) p. 54 22. R.D. Evans, The Atomic Nucleus, McGraw-Hill Book Co. (1955) p. 221 23. A. Bohr and B.R. Mottelson, Sov. J. Atom. Energy 14 (1963) 41 References (cont.) 102 Zk, S.A. Moszkowski, in Alpha-, Beta- and Gamma-Ray Spectroscopy, Edited by K. Siegbahn, North-Holland Pub. Co. (1968) p. 881 25. L.A. Sliv and I.M. Band, Coefficients of Internal Conversion of Gamma Radiation, Leningrad Physics-Technical Institute (1956) 26. J.R. Johnson, Ph.D. Thesis, University of British Columbia 27. L.K. Ng, Ph.D. Thesis, University of British Columbia 28. G.T. Ewan, in Progress in Nuclear Techniques and Instrumentation, Edited by F.J.M. Farley, North-Holland Pub. Co. vol .3 (1963) p. 123 

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