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Energy systematics of the giant gamow-teller resonance and a charge-exchange dipole spin-flip resonance
Volume 99B, number 5
PHYSICS LETTERS
5 March 1981
ENERGY SYSTEMATICS OF THE GIANT GAMOW-TELLER RESONANCE AND A CHARGE-EXCHANGE DIPOLE SPIN-FLIP RESONANCE D .J. HOREN and C.D. GOODMAN 1 Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA D.E. BAINUM Emporia State University, Emporia, KS 66801, USA C.C. FOSTER Indiana University, Bloomington, IN 47401, USA C. G A A R D E The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
C.A. GOULDING and M.B. G R E E N F I E L D Florida A &M University, Tallahassee, FL 32307, USA J. RAPAPORT and T.N. TADDEUCCI Ohio University, Athens, OH 45701, USA E. SUGARBAKER and T. MASTERSON University o f Colorado, Boulder, CO 80302, USA S.M. AUSTIN, A. GALONSKY and W. STERRENBURG Michigan State University, East Lansing, M148824, USA Received 21 October 1980
Energy systematics of the giant Gamow-Teller resonance and a charge-exchange resonance excited by a L = 1, S = 1 interaction are presented. Plots of the energy separation between each resonance and the IAS versus ( N - Z)/A can be represented approximately by linear functions.
In a series o f papers [ I - 5 ] in the early 1960's, Fuiita, Ikeda and Fujii explored the description of isobaric analogue states (IAS) in terms of proton p a r t i c l e neutron hole pairs (pfi) and subsequently hypothesized the existence o f a collective giant G a m o w - T e l l e r (GT) resonance to explain the hindrance of GT transitions in beta decay. In the absence of s p i n - o r b i t splitting, 1 Now at Indiana University.
the energy separation between the GT and IAS was predicted [ 2 - 4 ] to be approximately linear with (iV- Z)/A. These. workers [ 2 - 4 ] also pointed out the probable existence of additional collective resonances of the type Al > 0 and AS = 1, Bohr and Mottelson [6] have discussed the general features of collective modes of excitation involving spin degrees of freedom. The first experimental observation o f a giant GT resonance for N > Z nuclei was reported by Doering et al. [7] from 383
Volume 99B, number 5
PHYSICS LETTERS
a study o f the (p, n) reaction using incident energies of 25 to 45 MeV. In this work we report energy systematics for the giant GT resonance as well as a new resonance excited via a L = 1, S = 1 interaction. The availability of intermediate energy protons at the Indiana University Cyclotron Facility (IUCF) has served as an impetus for further investigations, b o t h experimental and theoretical, of the (p, n) reaction. Calculations in terms of an effective nucleon-nucleus interaction at intermediate energies have been made by a number of authors [8,9]. The isospin dependent part of the effective interaction is quite complicated and includes the following items: central, s p i n - s p i n , s p i n - o r b i t , and tensor in all multipoles. However, for the distorted wave impulse approximation (DWlA) in the limit of zero momentum transfer, only the terms with angular momentum transfer L -- 0 are important and contributions from s p i n - o r b i t and tensor are negligible. Furthermore, calculations have shown [8,9] that the strength of the central s p i n isospin component relative to the central isospin component increases by more than a factor o f two with increasing proton energy between Ep = 100 and 200 MeV. From measurements of zero degree cross sections at 120 MeV, Goodman et al. [10] have deduced values for the volume integrals of the central isospin and central spin-isospin potentials which agree within about 20% with the theoretical [9] calculations. In a study o f the 90Zr(p, n)9°Nb reaction at Ep = 120 MeV, Bainum et al. [11] measured neutron angular distributions and found in addition to the IAS and giant GT resonances which have L = 0, a resonance at an excitation of 17.9 MeV in 90Nb which had an angular distribution characteristic o f L = 1 transfer. The energy of the new L = 1 resonance was found to be below the expected position o f the analogue o f the giant electric dipole resonance (GEDR; 1 - , T= 5). It was suggested that the L = 1 resonance might be a 1 - , T = 4 resonance belonging to a multiplet which includes the analogue of the T = 5, GEDR. A similar L = 1 resonance was also observed by Horen et al. [12] in the 208pb(p,n)208Bi reaction at 120 and 160 MeV. The cross section of the L = 1 resonance at the first maximum was found to be comparable to that of the giant GT resonance at 0 ° and behaved similarly as a function of proton energy. Since the GT resonance is excited via the spin-isospin component of the effective interaction, it was argued [12] that excitation of 384
5 March 1981
the L = 1 resonance also involves S = 1. This then implies that the L = 1 resonance is of a charge-exchange dipole mode with spin flip and, hence, could have j , r =0-,1- or2-. We have used the swinger facility [13] at IUFC, protons with incident energies of 120, 160, and 200 MeV, and neutron flight paths of 6 0 - 7 0 m to study the energetics of the GT and L = 1 resonances for a number of targets with A / > 90. For some targets, angular distributions were measured in 2.5 ° intervals out to about 15 ° , while for others 5 ° intervals were used. Targets studied included 90,92,94Zr, 112,116,124Sn, 169Tm and 208pb. The targets were in the form of selfsupporting metallic foils with thicknesses between 4 0 - 1 8 0 mg/cm 2. Neutron time-of-flight spectra for 0 = 4.5 °, i.e., near a maximum [11,12] in the differential cross section fbr Al = 1, are shown in fig. 1. The results of detailed analyses of these data will be given elsewhere. Here, we focus attention on the energy systematics of the GT and L = 1 resonances. In fig. 2 we have plotted versus ( N - Z)M the energy differences between the giant GT and L = 1 resonances, respectively, and the IAS. The energies of the IAS and GT resonances have been determined from 0 ° spectra, and those for the L = 1 resonance from preliminary analyses of the 4.5 ° spectra. The uncertainties for E G T - E I A S are less than 0.4 MeV, and those for EA/= 1 -- EIA S are estimated to be ~< 1 MeV. As can be seen from the figure, to first order both energy differences can be represented by linear functions of (N-Z)~ A which have about the same slope. From fig. 2, we find the energy differences in MeV EGT - EIA s = - 3 0 . 0 ( N - Z)/A + 6.7 ,
(I a)
and
Ezxl=l - EIA S = - 3 3 . 0 ( N - Z)/A + 13.6.
(lb)
The GT-type excitations with L = 0, S= 1 involve mainly p~ excitations in which there is no change of radial wavefunctions, i.e., excitations within the same oscillator shell. The energies of these would lie close to those for the IAS except that an important contribution to the GT comes from transitions of the type (j = l+ 1/2) -+ (j = l - 1/2). Consequently, the GT energy is shifted up relative to the IAS b y an amount typical of this s p i n - o r b i t splitting. This accounts for the constant term in eq. ( l a ) . Now the residual p - f i interactions introduce a further shift which Fujita et al. [3] esti-
Volume 99B, number 5
PHYSICS LETTERS
160
I
900
En(MeV) ~80 2 0 0
e9Ozr
(p,n) TIME OF FLIGHT SPECTRA Ep= 2 0 0 MeV 8= 4.3 °
600
GT
300
[
14 - - I
I ~--F~
/
9OZr
5 March 1981
1
~
r
]
eg2Zr
t2 ....
e94Zr
,o
-- ~ i ~ . . . T ~
s >
6
--
4
--
0 >
EG T -Eiz~ S
90Zr
~ 9 e 2
600
I
--
Zr
GT ,
300 o
0.t0
~24 e.,,.,,.,.20S p b /
[
l
[
[
0/2
0.~4
0.16
0.t8
~n I -"'Z'A 0.20
0.22
[N- Z )/A 0
Fig. 2. Plots of (EGT - EIAS) and (EAd= ! - EIAS) versus ( N - Z)/A,
6OO
I
I
3OO c.)
0 600
~
~.=I
GT
r" 900 J
I AO:I
600
300
2O0
400 CHANNEL
600
800
mated to be about - 1 5 ( N - Z ) / A MeV, in reasonable agreement with what is observed. Gapanov and Lyutostanskii [14] have used the theory of finite Fermi systems and made microscopic calculations o f the excitation energies and strengths of the IAS and GT resonances for a number of nuclei from arsenic to lanthanum. Two values of the spin-isospin constant were considered, i.e., g~ = 1.0 and 1.3. Their predicted energy differences, EGT - EIAS, withg~) = I for l l 6 S n and 124Sn are in excellent agreement with our data (i.e., within 0.3 MeV); however, those for 90,92,94Zr fall on a parallel line about 2 MeV higher than our measured values [14]. The calculated energies [14] for the IAS resonances for both the Zr and Sn isotopes agree within a few tenths of an MeV with observed values. Hence, the discrepancy between the calculated and measured E G T - EIA S for the Zr isotopes indicates a problem with the calculated values o f E G y . This is probably not too surprising because such calculations are expected to be sensitive to a detailed knowledge o f the unperturbed p a r t i c l e - h o b wave functions Fig. 1. Time-of-flight spectra at 4.3 ° for the (p, n) reaction at E D = 200 MeV for targets of 9°Zr, 112Sn, 169Tm, Z24Sn, and "208pb. 385
Volume 99B, number 5
PHYSICS LETTERS
and energies which should be dependent upon the filling of shell model orbits. Examination of the microscopic calculations [13] seems to clearly show such effects. However, in view of the discrepancy for the Zr isotopes it would appear that additional data are needed to further examine this point. The k = 1, S = 1 response involves a change of parity and, consequently, the pn excitations are across one major shell. The constant in eq. ( l b ) is representative of an effective energy for a shell crossing to the s p i n - o r b i t partners which are available by AI - 1 transitions. The same residual p - f i interactions as for the GT would be expected to be operative here also, and this is about what is found empirically. At present we are unable to assign a definite jrr to the L = 1, S = 1 resonance, and it might contain components with all three values 0 - , 1 - and 2 - . Recently the theory of finite Fermi systems has also been employed by Krmpotic et at. [151 to calculate the charge-exchange dipole oscillations (with and without spin flip) for 208pb. For the spin flip transitions, they [15] find the main strength of the 0 resonance to be concentrated about 6.6 MeV above the 1AS, the 1 - about 6.0 MeV, and the 2 - resonance to be more fragmented with the largest component about 0.3 MeV above the 1AS (this is without folding in the spreading widths). The greater concentration of strength associated with the 1 - component would imply it should dominate the L = 1 structure. T h e p o s i tion of the L = 1 peak in fig. 1 is in qualitative agreement with this picture, but a detailed comparison will have to await final decomposition of the spectra and further analysis of the data. The same calculations [15] predict the 1 - , S = 0 resonance to be located about 2.9 MeV above the 1AS. At the proton energies used in this work we would not expect to populate significantly the latter, but it might appear in spectra at lower bombarding energies. A striking feature in fig. 2 is that the values of E a l = l - EIA S for the three Zr isotopes lie about 3 MeV above the curve formed by the other elements, Since at present there are no detailed calculations of a L = 1 , S = 1 resonance available for the Zr isotopes, one can only speculate as to the reasons for this. One might be that the distribution of strength among the J-components for the Zr isotopes differs from that for the other elements. Or, possibly, the effective energy for shell crossing in Zr is greater. (This might not be 386
5 March 1981
unreasonable from shell-model considerations.) In this work we have presented phenomenological systematics of the GT and a giant L = 1 resonance (both of which involve spin flip) for the medium to heavy mass region. Some agreement with calculations using finite Fermi systems has been found. However, much additional investigation remains before detailed comparisons can be made. We would like to thank Bill Lozowski and Tina Rife for fabricating many of the targets, and the staff of IUCF for providing the cyclotron operation and supporting functions. Theoretical discussions with Drs. W.G. Love, G.R. Satchler, and J. Speth are gratefully acknowledged. This work was supported in part by the Department of Energy, Division of Basic Energy Sciences under Contract No. W-7405-eng-26 with the Union Carbide Corporation, the National Science Foundation, and the Danish National Science Research Council. References
[1] K. Ikeda, S. Fujii and J.I. Fujita, Phys. Lett. 2 (1962) 169. [2] K. Ikeda, S. Fujii and J.I. Fujita, Phys. Lett. 3 (1963) 271. [3] .l.I. Fujita, S. Fujii and K. Ikeda, Phys. Rev. 133 (1964) B549. [4] K. Ikeda, Prog. Theor. Phys. 31 (1964) 434. [5 ! J.I. Fujita and K. lkeda, Nucl. Phys. 67 (1965) 145. [6] A. Bohr and B.R. Mottelson, Nucl. Structure, Vol. II (Benjamin, New York, 1969), [7] R.R. Doering,. A. Galonsky, D .M. Patterson and G.F. Bertsch, Phys. Rev. Lett. 35 (1975) 1961. [8] F. Petrovich, The (p, n) reaction and the nucleonnucleon force, eds. C.D. Goodman et al. (Plenum, New York, 1980) p. 115. [9] W.G. Love, The (p, n) reaction and the nucleon-nucleon force, eds. C.D. Goodman et al. (Plenum, New York, 1980) p. 23. [10] C.D. Goodman et al., Phys. Rev. Lett. 44 (1980) 1755. [11] D.E. Bainum et al., Phys. Rev. Lett. 44 (1980) 1751. [12] D.J. Horen et al., Phys. Lett. 95B (1980) 27. [13] C.D. Goodman et al., IEEE Trans. Nucl. Sci. NS-26 (1979) 2248. [14] Yu.V. Gaponov and Yu.S. Lyutostanskii, Yad. Fiz. 16 (1972) 484 [Soy. J. Nucl. Phys. 16 (1973) 270]; Yad. Fiz. 19 (1974) 62 [Soy. J. Nucl. Phys. 19 (1974) 33]. [15 ] F. Krmpotic, K. Ebert and W. Wild, Nucl. Phys. A342 (1980) 497.
PHYSICS LETTERS
5 March 1981
ENERGY SYSTEMATICS OF THE GIANT GAMOW-TELLER RESONANCE AND A CHARGE-EXCHANGE DIPOLE SPIN-FLIP RESONANCE D .J. HOREN and C.D. GOODMAN 1 Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA D.E. BAINUM Emporia State University, Emporia, KS 66801, USA C.C. FOSTER Indiana University, Bloomington, IN 47401, USA C. G A A R D E The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
C.A. GOULDING and M.B. G R E E N F I E L D Florida A &M University, Tallahassee, FL 32307, USA J. RAPAPORT and T.N. TADDEUCCI Ohio University, Athens, OH 45701, USA E. SUGARBAKER and T. MASTERSON University o f Colorado, Boulder, CO 80302, USA S.M. AUSTIN, A. GALONSKY and W. STERRENBURG Michigan State University, East Lansing, M148824, USA Received 21 October 1980
Energy systematics of the giant Gamow-Teller resonance and a charge-exchange resonance excited by a L = 1, S = 1 interaction are presented. Plots of the energy separation between each resonance and the IAS versus ( N - Z)/A can be represented approximately by linear functions.
In a series o f papers [ I - 5 ] in the early 1960's, Fuiita, Ikeda and Fujii explored the description of isobaric analogue states (IAS) in terms of proton p a r t i c l e neutron hole pairs (pfi) and subsequently hypothesized the existence o f a collective giant G a m o w - T e l l e r (GT) resonance to explain the hindrance of GT transitions in beta decay. In the absence of s p i n - o r b i t splitting, 1 Now at Indiana University.
the energy separation between the GT and IAS was predicted [ 2 - 4 ] to be approximately linear with (iV- Z)/A. These. workers [ 2 - 4 ] also pointed out the probable existence of additional collective resonances of the type Al > 0 and AS = 1, Bohr and Mottelson [6] have discussed the general features of collective modes of excitation involving spin degrees of freedom. The first experimental observation o f a giant GT resonance for N > Z nuclei was reported by Doering et al. [7] from 383
Volume 99B, number 5
PHYSICS LETTERS
a study o f the (p, n) reaction using incident energies of 25 to 45 MeV. In this work we report energy systematics for the giant GT resonance as well as a new resonance excited via a L = 1, S = 1 interaction. The availability of intermediate energy protons at the Indiana University Cyclotron Facility (IUCF) has served as an impetus for further investigations, b o t h experimental and theoretical, of the (p, n) reaction. Calculations in terms of an effective nucleon-nucleus interaction at intermediate energies have been made by a number of authors [8,9]. The isospin dependent part of the effective interaction is quite complicated and includes the following items: central, s p i n - s p i n , s p i n - o r b i t , and tensor in all multipoles. However, for the distorted wave impulse approximation (DWlA) in the limit of zero momentum transfer, only the terms with angular momentum transfer L -- 0 are important and contributions from s p i n - o r b i t and tensor are negligible. Furthermore, calculations have shown [8,9] that the strength of the central s p i n isospin component relative to the central isospin component increases by more than a factor o f two with increasing proton energy between Ep = 100 and 200 MeV. From measurements of zero degree cross sections at 120 MeV, Goodman et al. [10] have deduced values for the volume integrals of the central isospin and central spin-isospin potentials which agree within about 20% with the theoretical [9] calculations. In a study o f the 90Zr(p, n)9°Nb reaction at Ep = 120 MeV, Bainum et al. [11] measured neutron angular distributions and found in addition to the IAS and giant GT resonances which have L = 0, a resonance at an excitation of 17.9 MeV in 90Nb which had an angular distribution characteristic o f L = 1 transfer. The energy of the new L = 1 resonance was found to be below the expected position o f the analogue o f the giant electric dipole resonance (GEDR; 1 - , T= 5). It was suggested that the L = 1 resonance might be a 1 - , T = 4 resonance belonging to a multiplet which includes the analogue of the T = 5, GEDR. A similar L = 1 resonance was also observed by Horen et al. [12] in the 208pb(p,n)208Bi reaction at 120 and 160 MeV. The cross section of the L = 1 resonance at the first maximum was found to be comparable to that of the giant GT resonance at 0 ° and behaved similarly as a function of proton energy. Since the GT resonance is excited via the spin-isospin component of the effective interaction, it was argued [12] that excitation of 384
5 March 1981
the L = 1 resonance also involves S = 1. This then implies that the L = 1 resonance is of a charge-exchange dipole mode with spin flip and, hence, could have j , r =0-,1- or2-. We have used the swinger facility [13] at IUFC, protons with incident energies of 120, 160, and 200 MeV, and neutron flight paths of 6 0 - 7 0 m to study the energetics of the GT and L = 1 resonances for a number of targets with A / > 90. For some targets, angular distributions were measured in 2.5 ° intervals out to about 15 ° , while for others 5 ° intervals were used. Targets studied included 90,92,94Zr, 112,116,124Sn, 169Tm and 208pb. The targets were in the form of selfsupporting metallic foils with thicknesses between 4 0 - 1 8 0 mg/cm 2. Neutron time-of-flight spectra for 0 = 4.5 °, i.e., near a maximum [11,12] in the differential cross section fbr Al = 1, are shown in fig. 1. The results of detailed analyses of these data will be given elsewhere. Here, we focus attention on the energy systematics of the GT and L = 1 resonances. In fig. 2 we have plotted versus ( N - Z)M the energy differences between the giant GT and L = 1 resonances, respectively, and the IAS. The energies of the IAS and GT resonances have been determined from 0 ° spectra, and those for the L = 1 resonance from preliminary analyses of the 4.5 ° spectra. The uncertainties for E G T - E I A S are less than 0.4 MeV, and those for EA/= 1 -- EIA S are estimated to be ~< 1 MeV. As can be seen from the figure, to first order both energy differences can be represented by linear functions of (N-Z)~ A which have about the same slope. From fig. 2, we find the energy differences in MeV EGT - EIA s = - 3 0 . 0 ( N - Z)/A + 6.7 ,
(I a)
and
Ezxl=l - EIA S = - 3 3 . 0 ( N - Z)/A + 13.6.
(lb)
The GT-type excitations with L = 0, S= 1 involve mainly p~ excitations in which there is no change of radial wavefunctions, i.e., excitations within the same oscillator shell. The energies of these would lie close to those for the IAS except that an important contribution to the GT comes from transitions of the type (j = l+ 1/2) -+ (j = l - 1/2). Consequently, the GT energy is shifted up relative to the IAS b y an amount typical of this s p i n - o r b i t splitting. This accounts for the constant term in eq. ( l a ) . Now the residual p - f i interactions introduce a further shift which Fujita et al. [3] esti-
Volume 99B, number 5
PHYSICS LETTERS
160
I
900
En(MeV) ~80 2 0 0
e9Ozr
(p,n) TIME OF FLIGHT SPECTRA Ep= 2 0 0 MeV 8= 4.3 °
600
GT
300
[
14 - - I
I ~--F~
/
9OZr
5 March 1981
1
~
r
]
eg2Zr
t2 ....
e94Zr
,o
-- ~ i ~ . . . T ~
s >
6
--
4
--
0 >
EG T -Eiz~ S
90Zr
~ 9 e 2
600
I
--
Zr
GT ,
300 o
0.t0
~24 e.,,.,,.,.20S p b /
[
l
[
[
0/2
0.~4
0.16
0.t8
~n I -"'Z'A 0.20
0.22
[N- Z )/A 0
Fig. 2. Plots of (EGT - EIAS) and (EAd= ! - EIAS) versus ( N - Z)/A,
6OO
I
I
3OO c.)
0 600
~
~.=I
GT
r" 900 J
I AO:I
600
300
2O0
400 CHANNEL
600
800
mated to be about - 1 5 ( N - Z ) / A MeV, in reasonable agreement with what is observed. Gapanov and Lyutostanskii [14] have used the theory of finite Fermi systems and made microscopic calculations o f the excitation energies and strengths of the IAS and GT resonances for a number of nuclei from arsenic to lanthanum. Two values of the spin-isospin constant were considered, i.e., g~ = 1.0 and 1.3. Their predicted energy differences, EGT - EIAS, withg~) = I for l l 6 S n and 124Sn are in excellent agreement with our data (i.e., within 0.3 MeV); however, those for 90,92,94Zr fall on a parallel line about 2 MeV higher than our measured values [14]. The calculated energies [14] for the IAS resonances for both the Zr and Sn isotopes agree within a few tenths of an MeV with observed values. Hence, the discrepancy between the calculated and measured E G T - EIA S for the Zr isotopes indicates a problem with the calculated values o f E G y . This is probably not too surprising because such calculations are expected to be sensitive to a detailed knowledge o f the unperturbed p a r t i c l e - h o b wave functions Fig. 1. Time-of-flight spectra at 4.3 ° for the (p, n) reaction at E D = 200 MeV for targets of 9°Zr, 112Sn, 169Tm, Z24Sn, and "208pb. 385
Volume 99B, number 5
PHYSICS LETTERS
and energies which should be dependent upon the filling of shell model orbits. Examination of the microscopic calculations [13] seems to clearly show such effects. However, in view of the discrepancy for the Zr isotopes it would appear that additional data are needed to further examine this point. The k = 1, S = 1 response involves a change of parity and, consequently, the pn excitations are across one major shell. The constant in eq. ( l b ) is representative of an effective energy for a shell crossing to the s p i n - o r b i t partners which are available by AI - 1 transitions. The same residual p - f i interactions as for the GT would be expected to be operative here also, and this is about what is found empirically. At present we are unable to assign a definite jrr to the L = 1, S = 1 resonance, and it might contain components with all three values 0 - , 1 - and 2 - . Recently the theory of finite Fermi systems has also been employed by Krmpotic et at. [151 to calculate the charge-exchange dipole oscillations (with and without spin flip) for 208pb. For the spin flip transitions, they [15] find the main strength of the 0 resonance to be concentrated about 6.6 MeV above the 1AS, the 1 - about 6.0 MeV, and the 2 - resonance to be more fragmented with the largest component about 0.3 MeV above the 1AS (this is without folding in the spreading widths). The greater concentration of strength associated with the 1 - component would imply it should dominate the L = 1 structure. T h e p o s i tion of the L = 1 peak in fig. 1 is in qualitative agreement with this picture, but a detailed comparison will have to await final decomposition of the spectra and further analysis of the data. The same calculations [15] predict the 1 - , S = 0 resonance to be located about 2.9 MeV above the 1AS. At the proton energies used in this work we would not expect to populate significantly the latter, but it might appear in spectra at lower bombarding energies. A striking feature in fig. 2 is that the values of E a l = l - EIA S for the three Zr isotopes lie about 3 MeV above the curve formed by the other elements, Since at present there are no detailed calculations of a L = 1 , S = 1 resonance available for the Zr isotopes, one can only speculate as to the reasons for this. One might be that the distribution of strength among the J-components for the Zr isotopes differs from that for the other elements. Or, possibly, the effective energy for shell crossing in Zr is greater. (This might not be 386
5 March 1981
unreasonable from shell-model considerations.) In this work we have presented phenomenological systematics of the GT and a giant L = 1 resonance (both of which involve spin flip) for the medium to heavy mass region. Some agreement with calculations using finite Fermi systems has been found. However, much additional investigation remains before detailed comparisons can be made. We would like to thank Bill Lozowski and Tina Rife for fabricating many of the targets, and the staff of IUCF for providing the cyclotron operation and supporting functions. Theoretical discussions with Drs. W.G. Love, G.R. Satchler, and J. Speth are gratefully acknowledged. This work was supported in part by the Department of Energy, Division of Basic Energy Sciences under Contract No. W-7405-eng-26 with the Union Carbide Corporation, the National Science Foundation, and the Danish National Science Research Council. References
[1] K. Ikeda, S. Fujii and J.I. Fujita, Phys. Lett. 2 (1962) 169. [2] K. Ikeda, S. Fujii and J.I. Fujita, Phys. Lett. 3 (1963) 271. [3] .l.I. Fujita, S. Fujii and K. Ikeda, Phys. Rev. 133 (1964) B549. [4] K. Ikeda, Prog. Theor. Phys. 31 (1964) 434. [5 ! J.I. Fujita and K. lkeda, Nucl. Phys. 67 (1965) 145. [6] A. Bohr and B.R. Mottelson, Nucl. Structure, Vol. II (Benjamin, New York, 1969), [7] R.R. Doering,. A. Galonsky, D .M. Patterson and G.F. Bertsch, Phys. Rev. Lett. 35 (1975) 1961. [8] F. Petrovich, The (p, n) reaction and the nucleonnucleon force, eds. C.D. Goodman et al. (Plenum, New York, 1980) p. 115. [9] W.G. Love, The (p, n) reaction and the nucleon-nucleon force, eds. C.D. Goodman et al. (Plenum, New York, 1980) p. 23. [10] C.D. Goodman et al., Phys. Rev. Lett. 44 (1980) 1755. [11] D.E. Bainum et al., Phys. Rev. Lett. 44 (1980) 1751. [12] D.J. Horen et al., Phys. Lett. 95B (1980) 27. [13] C.D. Goodman et al., IEEE Trans. Nucl. Sci. NS-26 (1979) 2248. [14] Yu.V. Gaponov and Yu.S. Lyutostanskii, Yad. Fiz. 16 (1972) 484 [Soy. J. Nucl. Phys. 16 (1973) 270]; Yad. Fiz. 19 (1974) 62 [Soy. J. Nucl. Phys. 19 (1974) 33]. [15 ] F. Krmpotic, K. Ebert and W. Wild, Nucl. Phys. A342 (1980) 497.