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SPIN-FLIP ASYMMETRY IN THE PROTON INELASTIC SCATTERING TO THE FIRST 2+
STATES OF 48,50 Ti
M. Tomizawa, T. Aoki, Y. Aoki, T. Murayama, T. Sakai, Y. Tagishi, K. Yagi
To cite this version:
M. Tomizawa, T. Aoki, Y. Aoki, T. Murayama, T. Sakai, et al.. SPIN-FLIP ASYMMETRY IN
THE PROTON INELASTIC SCATTERING TO THE FIRST 2+ STATES OF 48,50 Ti. Journal de
Physique Colloques, 1990, 51 (C6), pp.C6-419-C6-422. �10.1051/jphyscol:1990642�. �jpa-00230909�
COLLOQUE DE PHYSIQUE
C o l l o q u e C6, s u p p l e m e n t au n 0 2 2 , Tome 51, 1 5 novembre 1990
SPIN-FLIP ASYMMETRY IN THE PROTON INELASTIC SCATTERING TO THE FIRST 2' STATES OF 8 , ~i
M. TOMIZAWA, T . AOKI, Y. AOKI, T. MURAYAMA*, T. SAKAI, Y. TAGISHI and K. YAGI
Institute of Physics and Tandem Accelerator Center, University of Fsukuba, Tsukuba, Ibaraki 305, Japan
Department of Physics, Tokyo University of Mercantile ~ a r i n e . K O ~ O - k u O Tokyo 135, Japan
RBsum6
Nous avons mesurB l e s distributions angulaires des sections efficaces d i f f e r e n t i e l l e s a ( 8 ) . du pouvoir d'analyse Ay ( 8 ) e t de l a probabilite de renversement du spin E ( 8 ) pour l e premier Btat 2' de 4 8 ~ i e t 5 0 ~ i , en u t i l i s a n t des faisceaux de protons polaris6s de 11 e t 18 MeV e t l a rBaction en coincidence (p,p'Y). Nous avons analyse l e s r e s u l t a t s en modele macroscopique (Bquations coupl6es sur des Btats vibrationnels) e t microscopique (DWBA, fonction d'onde du modgle en couche, force NN e f f e c t i v e ) .
Abstract - Angular distributions of the differential cross section a(@), analyzing power Ay(8), spin-flip probability S(8) and spin-flip asymmetry e(6') in the excitation of the first 2+ states in 48Ti and 50Ti were measured at incident energies of 11 and 18 MeV using (p,ply) coincidence technique with polarized proton beam. The results were analyzed in terms of a macroscopic coupled channels method based on the vibrational model and of the microscopic distorted wave Born approximation (DWBA) based on shell-model wave functions and effective nucleon-nucleon interactions.
A spin-flip asymmetry E ( B ) = (u+-(8) - u-+(8))/(u+-(8)
.+
u-+(8)) in a direct inelastic scattering of nucleons arises from the interference between the spin rndependent and spin dependent interactions in the adiabatic approximation if the time reversal invariant and parity conservation laws hold /I/. Therefore it is expected that the e(6') is sensitive to the spin-dependent part in the interaction which causes the inelastic scattering. We have measured the a(8), Ay(8), S(6') and ~ ( 6 ' ) for inelastic scattering from 48Ti and 50Ti leading to 48Ti(2:, 0.99 MeV and 50~i(2:, 1.55 MeV) at E p = l l and 18 MeV using the (p,ply) coincidence method /2/ with tb
e polarized proton beam 131. The reason why the target nuclei 48Ti and 50Ti were chosen is the following:(1) From a microscopic view-point on nuclear structure and nuclear interaction: The nucleus ''Ti(Z=22,N=28) has two protons outside the Z=20 closed shell and the N=28 closed shell, while the nucleus 48Ti(Z=22,N=26) is a two-proton particle and two-neutron hole nucleus. Thus we expect to have good shell-model wave functions of the nuclei based on the shells of f7p, f512, p312 and pljz. On the basis of this microscopic nuclear-structure wave functions, we can expect to extract the effective nucleon-nucleon interaction in the inelastic scattering process.
(2) From a macroscopic view-point: In the excitation of the first 2+ state, 48Ti shows much more collective nature in quadrupole surface vibration than 50Ti. Indeed the quadrupole deformation parameter
pZ
for 48Ti (50Ti) is p2=0.265 (0.175). Thus the excitation of the first 2+ states in the two nuclei is expected to involve very different coupling between spin and coIlective degree of freedom.The polarized proton beam was produced by a Lamb-shift type polarized ion source with a spin-filter at the Tandem Accelerator Center, University of Tsukuba (UTTAC) /4/. The 50Ti target was a self-supporting metallic foil with thickness of 900 p g / c m 2 , enriched to 68 % in 50Ti
,
and 24 % in 48Ti. The inelastically scattered protons from the first excited states of 48Ti(0.99 MeV) and 50Ti(1.55 MeV) were well separated from the difference of these energies. Measurements were carried out in a large scattering chamber. The scattered protons were detected by two or three pairs of solid state detectors which were placed on both sides of the beam direction at 20" or 30' intervals. The y-rays emitted vertically to the reaction plane were detected with a NaI(T1) crystal, 76 mm x 76 mm, mounted on a photomultiplier tube. A beam polarimeter based on the
4He reaction was placed downstream from the target /5/.
7Li(6,2h
aracteristic features of the measured observables were as follows:
(1) The spin-flip asymmetry ~ ( 0 ) has fairly large values for the 48Ti and "Ti targets at E p = l l and 18 MeV.
(2) The angular distributions of the spin-flip asymmetry e(6') has strong mass-number dependence compared with the other observables.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990642
C6-420 COLLOQUE DE PHYSIQUE
The macroscopic calculations based on a vibrational model were performed in terms of the coupled channels method /6/ (see Fig. 1). The optical potential used for the incident and exit channels has the standard fonn /7/. The Full-Thomas type interaction was used as the spin-dependent parts of the collective form factors. All of the nine parameters in the optical potential were searched to give best fits to the experimental cross section and analyzing power of the elastic scattering. The searched optical potential parameters are given in Table 1.
The deformation parameter
Pz
were fixed to the values obtained from the Coulomb-excitation experiments, P2=0.265 and 0.175 for 48Ti and 50Ti, respectively /8/. The deformation parameters ,B for the real, imaginary and Coulomb deformations were fixed to the values obtained from the Coulomb-excitation experiments. Three values of the spin-orbit deformation parameter,Pso=O,
/3 and 2P were examined so as to see the effect of the stren th of the spin-orbit deformation on the observables. The magnitude of o(0) for both "Ti and S'T~ are well reproduced by using the deformation parameter obtained from the Coulomb-excitation at both 11 and 18 MeV. The angular distributions of o(B), Ay(B) and S(0) are roughly reproduced in these calculations. The effect due to the strength of the spin-orbit deformation is negligibly small for o(0), Ay(0) and S(B). So the spin dependent observables, Ay(B) and S(B) are mainly generated from the spin-dependent part (spin-orbit force in the optical potential for the incident or exit channel. The calculated e(0)
b
is more sensitive to t e strength of the spin-orbit deformation parameter
Pso
than the Ay(0) and S(0) are. However, predicted e(0) is insensitive to the incident energy and target nucleus.The calculations of inelastic scattering based on the microscopic model were done by the computer code DWBA74 /9/. The nuclear-structure wave functions of 4sTi and 50Ti were obtained from the shell model calculation by Ogawa
/lo/.
The modified Kuo-Brown matrix elements /11/were adopted as the two body effective interaction. The spectroscopic amplitudes (one body transition density) derived from the calculation are shown in Table 2. First for the projectile-target interaction, a simplified nucleon-nucleon interaction which includes a spin-independent term and a spin-spin term as /12/
V(r) = (VO
+
I421.
&)f (r), (1)was used in our calculation, where f ( r ) is assumed to be Yukawa form with a range of 1 fm.
Results of the microscopic calculations of a($), Ay(B), S(0) and e(B) for 48Ti and 50Ti at Ep = 18 MeV are shown in Fig. 2, where Vo is fixed to 100 MeV which is determined to reproduce the experimental cross sections, and the ratio of the spin-dependent and spin-independent strength are taken as Vl/& = 0, 118 and 114 to see the effect of the spin-dependent interaction. As in the case of the previous macroscopic calculation, the a(@), Ay(B) and S(0) are not sensitive to the strength of the spin-dependent interaction. The predicted ~ ( 0 ) is similar to that of the collective model calculation, and cannot reproduce the observed target dependence. Next the isospin-dependent interaction was taken into account as /12/
where f ( r ) is assumed to be Yukawa form with a range of 1 fm as before. The relative strength of the spin independent and dependent term in Eq. (2) for the proton-neutron interaction is
T/o
= Voo - Vol = 11, and Vl = Vlo -=
1. For the proton-proton interaction, we have% = Voo
+
Val = 4, and Vl =+ K1
= -4, in unit of the strength of the spin-dependent term for the proton-neutron interaction 1131. The strength of the interaction used in the calculations was determined to reproduce the experimental cross sections. The calculations for 48Ti and 50Ti at 18 MeV are shown in Fig. 3. The effect of the isospin-dependent interaction is quite small for a(0), Ay(8) and S(B). But the predicted 4 0 ) is sensitive to the isospin-dependent interaction, which causes a large difference between 48Ti and 50Ti. Such a target dependence arises from the different contributions in proton-proton and proton-neutron interaction parts between 48Ti and 50Ti because of the difference in the microscopic nuclear structure.Further systematic experiments and analyses are necessary for investigating the relation between the spin-flip asymmetry and the nuclear structure involved.
Table 1. Opticd potential parameters used in the coupled channels calculation. Incident energies, well depths in MeV and lengths in fm.
Target Ep
Vo
WZ Vso ro rr rso a0 ar as0 48Ti 11 52.1 8.28 5.60 1.24 1.33 0.87 0.61 0.47 0.63Table 2. Spectroscopic amplitudes (one body transition density) between 0: and 2: states of 48Ti and 50Ti obtained from shell-model calculation.
one body 48Ti 50Ti
transitiondensity proton neutron proton neutron
D(f;,f$ -0.340 -0.593 0.630 -0.002
D(f$,P+) -0.194 -0.287 0.122 0.369
D(f;,fg) -0.023 -0.193 0.013 0.159
D(P$,P+) -0.018 -0.037 0.010 0.018
D(P?,f$) -0.013 -0.023 0.010 0.010
D ( f $ , f $ ) -0.004 -0.013 0.007 0.023
D(f$,P+) -0.009 -0.022 0.014 0.020
@ . ,.,
(deg.1 p - 0 . . .s.0.- pao.= 8- p - 2 p - . - . -
S.O. -
Fig. 1 Collective-model predictions of a($), Ay(0), S(0) and ~ ( 0 ) in the inelastic scattering to 2: state with the optical parameters of Table 1. The strength of the spin-orbit deformation was varied as
Pso=O, P
and 2P.COLLOQUE DE PHYSIQUE
Fig. 2 Microsco ic calculations of o(B), As(@), S(B) and
4).
The strength of the spin-independent force is fixed at 100 MeV, and that of the spin-spin interaction was varied as K/Vo=O, 118 and 114.Fig. 3 The effect of the isospin-dependent interaction on the observables.
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