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The ß-decay of 48Cr and low energy collective M1 transitions
Volume 197, number 4
PHYSICS LETTERSB
5 November 1987
THE [~-DECAY OF 4SCr AND LOW ENERGY COLLECTIVE M1 TRANSITIONS
M. ABDELAZIZ and J.P. ELLIOTT School of Mathematical and Physical Sciences, University of Sussex, Brighton, Sussex BN1 9QH, UK Received 17 June 1987;revised manuscript received 13 August 1987
A measured half-life for the 13-decay of 48Cr is used to provide information on the spin contribution to a collective isovector M 1 transition.
Low energy collective M1 transitions have been the subject of considerable interest [1-4], both experimental and theoretical. They have been described geometrically as a scissor mode [5] of neutrons moving relative to protons while in the interacting boson model [2] they involve a state of "mixed" symmetry implying that neutrons and protons are excited out of phase, in an isovector manner. These two descriptions have much in common and the effect is present [4,6] even in an elementary shell-model with a single j orbit. There is also some debate [7-10] about the relative contributions of spin and orbital parts of the M1 operator in such transitions. In this letter we use a Gamow-Teller [3decay half-life to provide more information on these questions. We consider the [3-decay of the 0 + ground state of 48Cr to the 1 + level at 421 keV in 48V. This is a Gamov-Teller transition with T = 0 in the initial state and T = I in 48V. From the measured [11] log =4.294 we can deduce the reduced matrix element 2
( 1 + Ill Z t ,
Pll0 + )
=0.0743,
(1)
using standard [ 12] [3-decay constants. The matrix element (1) is reduced with respect to both J and T in the notation of Racah. Although it has not yet been identified, there will be an isobaric analogue of this 1 + state at an excitation of about 6.2 MeV in 48Cr. Since the isovector spin operator for M 1 transitions is also given by Zit,s, the matrix element (1) therefore determines the spin contribution to the electro-
magnetic M1 transition 0 + ~ 1 + from the ground state of 48Cr to this isobaric analogue state. Using bare g values, the isovector spin part of the M1 operator is given by - 9.4#NZit=si, from which we deduce the "experimental" value from eq. (1) x/Bspin(M1, 0 + --* 1+ ) =0.74/~N •
(2)
It is appropriate to use bare values for both the [3decay and M 1 operators since the experimental value (1) necessarily gives the matrix element of E,tisi in the exact wave functions. By definition Bspi,(M1) refers to the contribution from the spin part of the real M 1 operator and (2) gives its matrix element in the exact wave functions. In deducing (2) from (1) we have assumed good isospin symmetry. Since 4SCr is unstable it is presumably difficult to measure the B(M1) in eq. (2) directly. Theoretically the 1 + state involved in the excitation (2) is of the collective type discussed in our first paragraph, corresponding to the 1+ states in the neighbouring nuclei 46Ti and 48Ti at 4.3 and 3.74 MeV, respectively. The excitation energy of 6.2 MeV i n 48Cr is somewhat greater than this because the 1+ state in 48Cr has a different isospin ( T = 1) from that of the ground state ( T = 0) whereas in 46Ti a n d 48Ti it is the same, T = 1 and T=2, respectively. An isovector excitation from a T = 0 ground state can only populate states with T-- 1. The value (2) is compared in table 1 with measurements in the titanium nuclei and with pure f7/2 shell-model calculations [6] using an empirical interaction deduced from 42Sc and bare g values. We
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
505
Volume 197, number 4
PHYSICS LETTERS B
Table 1 A comparison of reduced M I matrix elements x/B( M1, 0 ÷ ~ 1÷ ) in units of/zN with ~ Nucleus
44Ti 46Ti 48Ti 48Cr
5 November 1987
= ~/Bspi,(M l) + ~
.
Calculated (bare g-values)
Experiment ~/B,~,.(MI )
.~MI)
~m(M1)
0.36(4) a) 0.74
1.0(1 ) a) 0.71(3) b)
1.15 0.80 0.54 1.38
1.88 1.30 0.88 2.26
a) 46Tidata is taken from ref. [7]. b) 48Tidata from ref. [ 13].
give m a t r i x e l e m e n t s r a t h e r t h a n B ( M 1 ) , with ~)=x/Bsp,n(M1)+x/Borbi,(M1). It is seen that the n e w " e x p e r i m e n t a l " v a l u e for 48Cr is a b o u t twice that for 46Ti a n d that this ratio is c o n s i s t e n t with the calculated values. T h e a b s o l u t e v a l u e s o f Bspin(M1 ) are c o n s i s t e n t with the q u e n c h i n g factor o f a b o u t 0.6 f o u n d in m o r e d e t a i l e d shell-model calc u l a t i o n s [ 10,12,14]. Since the total B ( M 1 ) i n 48Cr is n o t k n o w n , we c a n n o t give a n e x p e r i m e n t a l v a l u e for the ratio o f spin a n d orbital c o n t r i b u t i o n s b u t the large " e x p e r i m e n t a l " v a l u e x/Bso~n ( M 1 ) = 0.74 /tN shows that the spin part is significant. It is quite close to the value 0.9/ZN given by the best available detailed shell-model c a l c u l a t i o n [10] w h i c h calculates also , j B o r b , ( M I )/x/Bsp~n(Ml) = 1.25. O n e o f us ( M . A . ) acknowledges f i n a n c i a l s u p p o r t f r o m the A l g e r i a n g o v e r n m e n t .
References [ 1] D. Bohle, A. Richter, W. Steffan, A.E.L. Dieperink, N. Lo Iudice, F. Palumbo and O. Scholten, Phys. Lett. B 137 (1984) 27.
506
[2] F. Iachello, Phys. Rev. Lett. 53 (1984) 1427. [3] W.D. Hamilton, A, Irback and J.P. Elliott, Phys. Rev. Lett. 53 (1984) 2469. [4] L. Zamick, Phys. Rev. C 31 (1985) 1955. [5] N. Lo ludice and F. Palumbo, Phys. Rev. Lett. 41 (1978) 1532. [ 6 ] J.A. Evans, J.P. Elliott and S. Szpikowki, Nucl. Phys. A 435 (1985) 317. [7] C. Djalahi, N. Marty, M. Morlet, A. Willis, J.C. Jourdain, D. Bohle, U. Hartmann, G. Kuchler, A. Richter, G. Caskey, G.M. Crawley and A. Galonsky, Phys. Lett. B 164 (1985) 269. [8] L. Zamick, Phys. Lett. B 167 (1986) 1. [9] O. Civitarese, A. Faessler and R. Najarov, preprint. [ 10 ] T. Oda, M. Hino and K. Muto, Phys. Len. B 190 (1987 ) 14. [ 11 ] D.E. Alburger, Nucl. Data Sheets 45 (1985) 557. [ 12] R.D. Lawson, Theory of the nuclear shell model (Clarendon, Oxford, 1980). [ 13] V.K. Rasmussen, Phys. Rev. C 13 (1976) 631. [ 14] M. Abdelaziz, J. Thompson, J.P. Elliott and J.A. Evans, to be published.
PHYSICS LETTERSB
5 November 1987
THE [~-DECAY OF 4SCr AND LOW ENERGY COLLECTIVE M1 TRANSITIONS
M. ABDELAZIZ and J.P. ELLIOTT School of Mathematical and Physical Sciences, University of Sussex, Brighton, Sussex BN1 9QH, UK Received 17 June 1987;revised manuscript received 13 August 1987
A measured half-life for the 13-decay of 48Cr is used to provide information on the spin contribution to a collective isovector M 1 transition.
Low energy collective M1 transitions have been the subject of considerable interest [1-4], both experimental and theoretical. They have been described geometrically as a scissor mode [5] of neutrons moving relative to protons while in the interacting boson model [2] they involve a state of "mixed" symmetry implying that neutrons and protons are excited out of phase, in an isovector manner. These two descriptions have much in common and the effect is present [4,6] even in an elementary shell-model with a single j orbit. There is also some debate [7-10] about the relative contributions of spin and orbital parts of the M1 operator in such transitions. In this letter we use a Gamow-Teller [3decay half-life to provide more information on these questions. We consider the [3-decay of the 0 + ground state of 48Cr to the 1 + level at 421 keV in 48V. This is a Gamov-Teller transition with T = 0 in the initial state and T = I in 48V. From the measured [11] log =4.294 we can deduce the reduced matrix element 2
( 1 + Ill Z t ,
Pll0 + )
=0.0743,
(1)
using standard [ 12] [3-decay constants. The matrix element (1) is reduced with respect to both J and T in the notation of Racah. Although it has not yet been identified, there will be an isobaric analogue of this 1 + state at an excitation of about 6.2 MeV in 48Cr. Since the isovector spin operator for M 1 transitions is also given by Zit,s, the matrix element (1) therefore determines the spin contribution to the electro-
magnetic M1 transition 0 + ~ 1 + from the ground state of 48Cr to this isobaric analogue state. Using bare g values, the isovector spin part of the M1 operator is given by - 9.4#NZit=si, from which we deduce the "experimental" value from eq. (1) x/Bspin(M1, 0 + --* 1+ ) =0.74/~N •
(2)
It is appropriate to use bare values for both the [3decay and M 1 operators since the experimental value (1) necessarily gives the matrix element of E,tisi in the exact wave functions. By definition Bspi,(M1) refers to the contribution from the spin part of the real M 1 operator and (2) gives its matrix element in the exact wave functions. In deducing (2) from (1) we have assumed good isospin symmetry. Since 4SCr is unstable it is presumably difficult to measure the B(M1) in eq. (2) directly. Theoretically the 1 + state involved in the excitation (2) is of the collective type discussed in our first paragraph, corresponding to the 1+ states in the neighbouring nuclei 46Ti and 48Ti at 4.3 and 3.74 MeV, respectively. The excitation energy of 6.2 MeV i n 48Cr is somewhat greater than this because the 1+ state in 48Cr has a different isospin ( T = 1) from that of the ground state ( T = 0) whereas in 46Ti a n d 48Ti it is the same, T = 1 and T=2, respectively. An isovector excitation from a T = 0 ground state can only populate states with T-- 1. The value (2) is compared in table 1 with measurements in the titanium nuclei and with pure f7/2 shell-model calculations [6] using an empirical interaction deduced from 42Sc and bare g values. We
0370-2693/87/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
505
Volume 197, number 4
PHYSICS LETTERS B
Table 1 A comparison of reduced M I matrix elements x/B( M1, 0 ÷ ~ 1÷ ) in units of/zN with ~ Nucleus
44Ti 46Ti 48Ti 48Cr
5 November 1987
= ~/Bspi,(M l) + ~
.
Calculated (bare g-values)
Experiment ~/B,~,.(MI )
.~MI)
~m(M1)
0.36(4) a) 0.74
1.0(1 ) a) 0.71(3) b)
1.15 0.80 0.54 1.38
1.88 1.30 0.88 2.26
a) 46Tidata is taken from ref. [7]. b) 48Tidata from ref. [ 13].
give m a t r i x e l e m e n t s r a t h e r t h a n B ( M 1 ) , with ~)=x/Bsp,n(M1)+x/Borbi,(M1). It is seen that the n e w " e x p e r i m e n t a l " v a l u e for 48Cr is a b o u t twice that for 46Ti a n d that this ratio is c o n s i s t e n t with the calculated values. T h e a b s o l u t e v a l u e s o f Bspin(M1 ) are c o n s i s t e n t with the q u e n c h i n g factor o f a b o u t 0.6 f o u n d in m o r e d e t a i l e d shell-model calc u l a t i o n s [ 10,12,14]. Since the total B ( M 1 ) i n 48Cr is n o t k n o w n , we c a n n o t give a n e x p e r i m e n t a l v a l u e for the ratio o f spin a n d orbital c o n t r i b u t i o n s b u t the large " e x p e r i m e n t a l " v a l u e x/Bso~n ( M 1 ) = 0.74 /tN shows that the spin part is significant. It is quite close to the value 0.9/ZN given by the best available detailed shell-model c a l c u l a t i o n [10] w h i c h calculates also , j B o r b , ( M I )/x/Bsp~n(Ml) = 1.25. O n e o f us ( M . A . ) acknowledges f i n a n c i a l s u p p o r t f r o m the A l g e r i a n g o v e r n m e n t .
References [ 1] D. Bohle, A. Richter, W. Steffan, A.E.L. Dieperink, N. Lo Iudice, F. Palumbo and O. Scholten, Phys. Lett. B 137 (1984) 27.
506
[2] F. Iachello, Phys. Rev. Lett. 53 (1984) 1427. [3] W.D. Hamilton, A, Irback and J.P. Elliott, Phys. Rev. Lett. 53 (1984) 2469. [4] L. Zamick, Phys. Rev. C 31 (1985) 1955. [5] N. Lo ludice and F. Palumbo, Phys. Rev. Lett. 41 (1978) 1532. [ 6 ] J.A. Evans, J.P. Elliott and S. Szpikowki, Nucl. Phys. A 435 (1985) 317. [7] C. Djalahi, N. Marty, M. Morlet, A. Willis, J.C. Jourdain, D. Bohle, U. Hartmann, G. Kuchler, A. Richter, G. Caskey, G.M. Crawley and A. Galonsky, Phys. Lett. B 164 (1985) 269. [8] L. Zamick, Phys. Lett. B 167 (1986) 1. [9] O. Civitarese, A. Faessler and R. Najarov, preprint. [ 10 ] T. Oda, M. Hino and K. Muto, Phys. Len. B 190 (1987 ) 14. [ 11 ] D.E. Alburger, Nucl. Data Sheets 45 (1985) 557. [ 12] R.D. Lawson, Theory of the nuclear shell model (Clarendon, Oxford, 1980). [ 13] V.K. Rasmussen, Phys. Rev. C 13 (1976) 631. [ 14] M. Abdelaziz, J. Thompson, J.P. Elliott and J.A. Evans, to be published.