Search

A number of 6 − and 5 − states in 26 Al were studied in the region of excitation energy 5–15 MeV with the 24 Mg(α, d) 26 Al reaction at E α = 63.7 MeV. The data were analyzed within the framework of zero-range DWBA theory for a macroscopic deuteron-cluster transfer as well as for a microscopic two-nucleon transfer, and compared with our previous results on the 25 Mg( 3 He, d) 26 Al reaction. Several 6 − and 5 − states are newly proposed. Five 6 − states previously assigned as T = 1 were weakly observed in the present (α, d) reaction, which should excite only T = 0 states. The isospin breaking (α, d) transition to the 6 − 1 , T = 1 state was found to be an order of magnitude larger than a second-order exact-finite-range DWBA calculation for the successive transfer processes of ( α - 3 He-d) and ( α -t-d).

Differential cross sections and analyzing powers have been measured for (p, d) reactions on 1p, 2s, 1d, 2p, 1g and 2d shell nuclei with 65 MeV polarized protons. The analyzing powers clearly show a j -dependence which depends on the numbers of nodes in the radial wave function of the neutron. The shapes of the angular distributions of the analyzing powers can be classified into five types for simple neutron pickup reactions from the 1p−2d shells. The pickup from the 1 p 1 2 shell is singular.The DWBA calculations have been carried out on these (p, d) reactions in order to interpret the j -dependence. Adiabatic deuteron optical potentials can describe the data better than those derived from the deuteron elastic scattering except for the pickup from the 1 p 1 2 shell. The analyzing powers for the 1 p 1 2 shell neutron pickup can be reproduced only when large values of the radius and diffuseness parameters are used in the bound-state potential.

Low-lying octupole states of doubly-even 78–86Kr isotopes have been studied with inelastic scattering of 51.9 MeV protons. It is shown that in the doubly-even nuclei from Ge to Sr with N = 42–50, the lowest octupole vibrational energies of nuclei with equal neutron excess are almost the same. The transition strengths of these states increase with Z.

The in-plane α-α angular correlation of the reaction 12C(α, α')12C(4+)(α)8Be(0+) has been measured at an incident energy of 65 MeV. The correlation data were analyzed by coupled channel calculations on the basis of a rotator model. A strong sensitivity of the correlation function to the sign of the quadrupole and hexadecapole deformation parameters was found. The deformation parameters for 12C were determined to be β2 = −0.40±0.02 and β4 = +0.16±0.03.

Cross sections and analyzing powers in proton inelastic scattering leading to unnatural parity states of ${2}^{\ensuremath{-}}$, $T=0$ (6.025 and 6.75 MeV), ${2}^{\ensuremath{-}}$, $T=1$ (8.42 MeV) in $^{40}\mathrm{Ca}$ and ${6}^{\ensuremath{-}}$, $T=0$ (11.58 MeV) and ${6}^{\ensuremath{-}}$, $T=1$ (14.36 MeV) in $^{28}\mathrm{Si}$ were measured at 65 MeV. These states are pair states of different isospin with the same spin and parity. The analyzing powers for a pair of $T=0$ and $T=1$ excitations in $^{40}\mathrm{Ca}$ show an isospin dependence not observed in $^{28}\mathrm{Si}$. The measured angular distributions were compared with microscopic distorted-wave Born approximation calculations using two versions of the effective nucleon-nucleon interaction. As expected, the interaction emphasizing the tensor contribution predicts analyzing powers and cross sections in better agreement with the experimental data. As factors to produce a difference in the analyzing powers between the $T=0$ and the $T=1$ states, the effect of two transferred orbital angular momentum amplitudes allowed in a transition and the energy dependence of the isoscalar spin-dependent terms in the effective interaction are discussed.NUCLEAR REACTIONS $^{40}\mathrm{Ca}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{40}\mathrm{Ca}$, $^{28}\mathrm{Si}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{28}\mathrm{Si}$, $^{24}\mathrm{Mg}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}, {p}^{\ensuremath{'}})^{24}\mathrm{Mg}$, $E=65$ MeV, unnatural parity states of ${E}_{x}=6\ensuremath{-}15$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, analyzing power ${A}_{y}(\ensuremath{\theta})$, resolution \ensuremath{\sim}35 keV, DWBA analysis.

High spin states in the 2s-1d shell nuclei of 18F, 20F, 22Na, 24Na, 26Al, and 30P have been investigated by (α, d) reactions at incident energies of 64.3–65.3 MeV. The ( f 7 2 ) 2 7 + states in 20F, 22Na and 24Na, and the ( f 7 2 d 5 2 )6 − states in 20F and 24Na are proposed. The systematic dependenc of the Q-value and intensity on the mass number for the (α, d) reaction leading to the 5+, 6−, and 7+ states is obtained. For the 7+ states, the dependence of the Q-values on the mass number in the mass region below 26 deviates from the line expected from the results of heavier 2s-1d shell nuclei. The excitation energies of the ( f 7 2 ) 2 7 + states expected from a crude shell-model calculation are in good agreement with the experimental data. Using the Q-values for the 7+ states and empirical binding energies for the single-particle f 7 2 shell orbit, a mass dependency of the p-n interaction energies for the ( f 7 2 ) 2 7 + configuration has been found to be E[( f 7 2 ) 2 7 + ] = − 100 A of these 2s-1d shell nuclei.

Measurements of angular distributions of the cross sections and analyzing powers for the elastic and inelastic scatterings of 65 MeV polarized protons from $^{12}\mathrm{C}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$ are reported. Coupled channels analyses of the scattering data are presented assuming the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${4}_{1}^{+}$ states to be members of the ground band, the ${0}_{2}^{+}$ state to begin the\ensuremath{\beta} band, and the ${3}_{1}^{\mathrm{\ensuremath{-}}}$ state to begin the ${K}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ band in $^{12}\mathrm{C}$; the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${4}_{1}^{+}$ states to comprise the ground band, the ${2}_{2}^{+}$, ${3}_{1}^{+}$, and ${4}_{2}^{+}$ states to comprise the \ensuremath{\gamma} band, the ${3}_{1}^{\mathrm{\ensuremath{-}}}$ state to begin the ${K}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ band, and the ${1}_{1}^{\mathrm{\ensuremath{-}}}$ and ${3}_{2}^{\mathrm{\ensuremath{-}}}$states to comprise the ${k}^{\ensuremath{\pi}}$${=0}^{\mathrm{\ensuremath{-}}}$ band in $^{24}\mathrm{Mg}$; and the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${4}_{1}^{+}$ states to comprise the ground band, the ${0}_{2}^{+}$ state to begin the \ensuremath{\beta} band, the ${3}_{1}^{\mathrm{\ensuremath{-}}}$, ${4}_{1}^{\mathrm{\ensuremath{-}}}$, ${5}_{1}^{\mathrm{\ensuremath{-}}}$, and ${6}_{1}^{\mathrm{\ensuremath{-}}}$ states to comprise the ${k}^{\ensuremath{\pi}}$${=3}^{\mathrm{\ensuremath{-}}}$ band, and the ${1}_{1}^{\mathrm{\ensuremath{-}}}$and ${3}_{1}^{\mathrm{\ensuremath{-}}}$ states to comprise the ${K}^{\ensuremath{\pi}}$${=0}^{\mathrm{\ensuremath{-}}}$ band in $^{28}\mathrm{Si}$. The fit of the analyzing power of the \ensuremath{\beta} band ${0}_{2}^{+}$ level is improved by mixing the breathing mode of oscillation into the \ensuremath{\beta} vibration. Coupled channels analyses of the experimental angular distributions are presented for the levels in $^{32}\mathrm{S}$ in which the ${0}_{1}^{+}$, ${2}_{1}^{+}$, and ${4}_{1}^{+}$ states were assumed to belong to the ground band, the ${0}_{2}^{+}$ and ${2}_{3}^{+}$ states to the \ensuremath{\beta} band, the ${2}_{2}^{+}$, ${3}_{1}^{+}$,and ${4}_{2}^{+}$ states to the \ensuremath{\gamma} band, the ${3}^{\mathrm{\ensuremath{-}}}$ state to the ${3}^{\mathrm{\ensuremath{-}}}$ band, and the ${1}^{\mathrm{\ensuremath{-}}}$ state to the ${0}^{\mathrm{\ensuremath{-}}}$ band. These states were treated assuming a symmetric rotator model. The coupled channels calculations in terms of a vibrational model were also performed for $^{32}\mathrm{S}$. Multipole moments obtained from present data are compared to the moments deduced from hadron scattering and electromagnetic measurements. Transition strengths deduced from the (p,p') scattering are compared with gamma-ray decay widths for ${2}^{+}$ states in the ground bands.

The $^{16}\mathrm{O}$($^{6}\mathrm{Li}$,$d$)$^{20}\mathrm{Ne}$ and $^{28}\mathrm{Si}$($^{6}\mathrm{Li}$,$d$)$^{32}\mathrm{S}$ reactions have been studied at 75-MeV bombarding energy. The angular distributions have been analyzed with exact finite-range distorted-wave Born approximation calculations assuming a direct $\ensuremath{\alpha}$-cluster transfer. The calculations account for the shapes of the experimental angular distributions reasonably well. For the $^{16}\mathrm{O}$($^{6}\mathrm{Li}$,$d$)$^{20}\mathrm{Ne}$ reaction, the extracted relative $\ensuremath{\alpha}$-particle spectroscopic factors for the $^{20}\mathrm{Ne}$ ground state band are in good agreement with theoretical predictions, while those for the ${\mathrm{O}}^{\ensuremath{-}}$ excited band are in disagreement with them. For the $^{28}\mathrm{Si}$($^{6}\mathrm{Li}$,$d$)$^{32}\mathrm{S}$ reaction, spectroscopic factors are extracted for low-lying states of $^{32}\mathrm{S}$ and compared with those from other $\ensuremath{\alpha}$-transfer reactions. Some strongly populated states have been observed at high excitation energies of $^{32}\mathrm{S}$.NUCLEAR REACTIONS $^{16}\mathrm{O}$($^{6}\mathrm{Li}$,$d$)$^{20}\mathrm{Ne}$, $^{28}\mathrm{Si}$($^{6}\mathrm{Li}$,$d$)$^{32}\mathrm{S}$, $E=75$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, DWBA analysis spectroscopic factors.

The reactions ( 3 He, t), ( 3 He, 3 He), ( 3 He, α) and ( 3 He, d) on 48 Ca have been studied at an incident energy of 82 MeV. The obtained angular distributions for the ( 3 He, t) reaction have been analyzed in terms of second-order DWBA theory, using a zero-range approximation. The relative ratio of the cross sections for the excitation of the f in 7 2 f 7 2 −1 multiplets of 48 Sc could not be explained consistently by the one-step charge-exchange process only. However, the ratio was reproduced in order of magnitude by second-order DWBA calculations including the effect of two-step processes, such as ( 3 He-α-t) and ( 3 He-d-t) channels. The effects of the d- and α-channels on the elastic scattering of 3 He from 48 Ca were also examined in the framework of second-order full finite-range DWBA.

Differential cross sections and analyzing powers in inelastic scattering of 65- and 50-MeV polarized protons exciting the 1/sup +/ states at 12.71 MeV (T = 0) and 15.11 MeV (T = 1) in /sup 12/C have been measured. There is a marked difference between the analyzing powers of the two states, which show an out-of-phase pattern in angular distribution. The exchange effect was found to contribute essentially to the isospin dependence from the results of distorted-wave Born-approximation calculations.

The level schemes of the even 74–82 Se up to E x = 5.0 MeV have been investigated with high-resolution inelastic proton scattering at E p = 64.8 MeV. Several 4 + states with comparable strengths were found at E X = 2.0–5.0 MeV in all isotopes studied. The energy weighted sum-rule fraction of the 4 + states in this region increases with decreasing neutron number from 82 Se (1.0%) up to 76 Se (3.7%), and then decreases in 74 Se (2.6%). A RPA calculation with a pairing plus hexa-decapole-hexadecapole interaction can well reproduce the distribution of the excitation energies and transition strengths for the hexadecapole states.

Level structure of 76 Kr has been studied with the 78 Kr(p, t) 76 Kr reaction. Several low-lying levels were observed for the first time and the previously unknown mass excess of 76 Kr was measured to be 68 968 ± 15 keV. The measured angular distributions were compared with the predictions of DWBA calculations and the spin-parities of some of the levels are proposed. The level structure of 76 Kr are compared with those of other N = 40 isotones, and discussed in terms of several nuclear models.

The /sup 18/O(/sup 6/Li,d)/sup 22/Ne reaction has been studied at 72-MeV bombarding energy. The angular distributions for transitions to low-lying states in /sup 22/Ne are fitted by exact finite-range distorted-wave Born approximation calculations and yield relative spectroscopic factors in good agreement with theoretical predictions.

Absolute values of the polarization in p-12C elastic scattering have been measured at 60.0 and 64.5 MeV at 47.5° in the laboratory system using a double scattering method and a method to measure an asymmetry with a polarized beam. The results are P(60.0 MeV, 47.5°) = 0.965 ± 0.011 and P(64.5 MeV, 47.5°) = 0.975 ± 0.11. Based on these values, the polarization measurements have been extended to the energy range from 40–75 MeV at several angles round 47.5° using the polarized proton beam and the energy degrader. Differential cross sections and polarizations from 15–115° are also presented at 65 MeV. These data will be valuable for the monitoring of beam polarization in this energy region.

Two low-lying octupole states of 78,80,82Kr, which were previously observed in inelastic proton scattering to share the low-lying octupole vibrational strength, were found to be strongly excited in the (p,t) reaction. Characteristics of these states and a comparison with the IBM model strongly suggest that the splittings in the lighter isotopes 76,78,80,82Kr are due to a coupling of the octupole vibration to the quadrupole degree of freedom.

Differential cross sections and analyzing powers of the /sup 13/C( p,t)/sup 11/C and /sup 13/C( p,/sup 3/He)/sup 11/B reactions to the ground and the first excited states were measured at E/sub p/ = 65 MeV. They were analyzed by means of distorted-wave Born approximation calculations including both one- and two-step processes of p-d-t or -/sup 3/He. Attention was paid to an isospin symmetry of the reaction process consisting of both isospin 0 and 1 channels, which were important in a comparable order. As intermediate states of /sup 12/C in the sequential process, five states of either isospin 0 or 1, which were strongly excited by the /sup 13/C( p,d)/sup 12/C reaction, were taken into account. A good fit between the data and the theoretical values was obtained, especially for the ( p,t) reactions, concerning both differential cross sections and analyzing powers. The calculations including one-step and sequential processs induced, in some cases, remarkable differences from the one-step calculation for backward angles.

The 27 Al(α, t) and (α, 3 He) reactions have been measured at E α = 64.5 MeV. The experimental angular distributions were analyzed by the exact finite-range DWBA calculations assuming a nucleon stripping mechanism. The distributions of spectroscopic strengths for the single-particle transitions with transferred angular momenta l = 0, 1, 2, 3 and 4 have been obtained. The strengths for the transitions to the stretched 6 − states in 28 Si and 28 Al are compared to those obtained from inelastic scattering on 28 Si. The present results show no distinctive differences in the structures for 6 − T = 0 and 1 states in 28 Si such as are observed in proton and pion inelastic scattering on 28 Si.

The 2+2 and 4+1 states of the even isotopes 78–86Kr have been studied by the inelastic scattering of protons. The B(E2;0+g → 2+2) values of these isotopes are roughly equal, where as the B(E4;+g → 4+1) values decrease to a minimum at 82Kr and then increase with neutron number. Comparison of the experimental results with current theoretical models implies an abrupt change of structure between 78–82Kr and 84–86Kr.

The 24, 26 Mg( 6 Li, d) 28, 30 Si reactions have been studied at 73 MeV bombarding energy. The angular distributions were analyzed with exact finite-range distorted wave Born approximation calculations assuming a direct α-cluster transfer. Extracted spectroscopic strengths leading to low-lying levels of 28 Si and relative spectroscopic strengths between transitions to 28 Si and 30 Si ground states are consistent with those previously obtained by several α-transfer reactions. Many strongly populated levels have been observed at E x ≳ 10 MeV for 28 Si. A marked similarity was found between the deuteron spectrum and the 24 Mg(α, α) 24 Mg excitation function in this excitation energy region. A brief comparison of the present α-transfer results with previous two-nucleon transfer data leading to 28,30 Si is also presented.

Differential cross sections and vector analyzing powers were measured for the (d, p) reaction with 56 MeV polarized deuterons. The investigation covered the transitions to the single-particle states of the 1p. 2s, 1d. 2p, 1f, 3s, 2d and 1g shells. The analyzing powers showed a j -dependence which depended on the number of nodes in the radial wave function of the transferred neutron. DWBA and adiabatic model calculations were carried out. The DWBA calculations reproduced the experimental cross sections and analyzing powers for the stripping to the j > states. The adiabatic model did not necessarily improve the fits to the data for these transitions. As for the j transitions, on the other hand, the DWBA calculations could not reproduce the experimental angular distributions, while the adiabatic model calculations improved the agreement with the experimental data.

The angular distributions of the reaction 16 O( 6 Li, d) 20 Ne at 75 MeV for transitions to members of the ground state band are well fitted by exact finite-range DWBA calculations assuming a direct α-cluster transfer and yield spectroscopic factors in good agreement with shell-model predictions.

The form factor for a three-particle transfer reaction such as the (p, α) reaction is constructed by extending the Bayman and Kallio procedure for integrating over internal coordinates. The C13(p→,α)10Bgs reaction at Ep = 65 MeV is analyzed using this method.

For an injector cyclotron to a ring cyclotron proposed at RCNP, the second, third and fourth harmonic modes are used for the light ion acceleration. To accelerate ions in these harmonic modes without phase space deformation, it is necessary to investigate the effect of radial-longitudinal coupling. For single, two and three dee configurations, the beam behavior in radial phase space was studied numerically for each harmonic mode and dee angle. In the case of the second and third harmonic accelerations of protons with two dees, dee angles between 60 and 75 degrees are acceptable. The results are compared with 180-degree single dee and 40-degree three dees for the third harmonic mode.

Differential cross sections and analyzing powers have been measured for (p, d) reactions on 1p,2s,1d,1f,2p,1g and 2d shell nuclei with 65 MeV polarized protons. The analyzing powers clearly show a j‐dependence which depends on the numbers of nodes in the radial wave function of the neutron. The shapes of the angular distributions of the analyzing powers can be classified into five types for simple neutron pickup reactions from these shells. The pickup from the 1p1/2 shell is singular. The analyzing powers for the 1p1/2 shell neutron pickup can be reproduced by DWBA calculations only when large values of the radius and diffuseness parameters are used in the bound state potential.

The angular distributions of cross sections and analyzing powers for proton inelastic scattering leading to the 11.58 MeV and 14.36 MeV states in 28Si and the 15.15 MeV state in 24Mg have been measured with 65 MeV polarized proton beam using the spectrograph RAIDEN. Preliminary microscopic DWBA calculations including exchange process have been performed. The results are discussed.