The (t,p) reaction on the zinc isotopes

Multichannel spectrograph studies of the (t, p) reaction on the Zn isotopes have provided energy-level data, cross-section measurements and many new spin and parity determinations. The systematics of the energy spectra of the even zinc isotopes are discussed.     

The (t,p) reaction on the even isotopes of neodymium

The Aldermaston multi-angle magnetic spectrograph and tandem Van de Graaff accelerator have been used to study the (t, p) reactions leading to the neodymium isotopes ^{144,146,148,150, 152}Nd bombarding energy of 13 MeV. The Q-values were measured for final states with excitation energies up to about 3 MeV.     

The (t,p) reaction to the low-lying levels of the zirconium isotopes

The (t, p) reaction on the isotopes ^90,92,94,96Zr has been carried out at a bombarding energy of 20 MeV. Only weakly excited O⁺ states are observed in ⁹²Zr and ⁹⁴Zr while the first excited O⁺ state in ⁹⁶Zr is strongly excited. No O⁺ states are seen in ⁹⁸Zr. The results indicate a trend for ground state excitations intermediate between simple shell model and pairing vibration theory. The low-lying levels of ⁹²Zr and ⁹⁴Zr are described by detailed shell model calculations. There is no indication in these nuclei of the rapid onset of deformation previously reported in ¹⁰⁰Zr, nor is there any evidence for an excited rotational band structure in any of the zirconium nuclei studied.     

Study of even-mass Ba nuclei by the (p,t) reaction

The (p, t) reaction on the nuclei ^{134, 136, 138}Ba has been studied at a bombarding energy of 52 MeV. Angular distributions of emitted tritons were obtained between 6° and 60°. The following six negative-parity states were strongly excited by the (p, t) reaction: 5^?(2.121 MeV) and 7^?(2.482 MeV) in ¹³²Ba, 5^?(1.998 MeV) and 7^?(2.274 MeV) in ¹³⁴Ba, and 5^?(2.139 MeV) and 7^?(2.031 MeV) in ¹³⁶Ba. DWBA calculations using the code DWUCK successfully reproduce these angular distributions. The 0⁺ assignment to the 1.761 MeV level in ¹³⁴Ba is confirmed. Intensities of the (p, t) reaction for low-lying states are discussed.     

Study of the W(t, p)W reaction at 20 MeV

The ¹⁸²W(t, p)¹⁸⁴W reaction has been studied at 20 MeV. The outgoing protons were detected in an Elbek broad range magnetic spectrograph. Absolute cross sections and angular distributions were measured. Evidence for inelastic effects in the reaction mechanism was observed for the first excited 2⁺ state, the 3⁻ level at 1221 keV and the 5⁺ state at 1295 keV. The 0⁺ level at 1002 keV was populated with ≈ 2% the ground state cross section. A 4⁺ level at 1536 keV was observed with ≈ 50% the ground state cross section. Calculations of the absolute (t, p) cross sections to this and other states with known structure resulted in excellent agreement with the measured values.     

Energy levels in even actinide isotopes from (t,p) reactions

Energy levels in^{232, 234}Th,^{236, 238, 240}U and in²⁵⁰Cm have been measured using the (t, p) reaction. Angular distributions were obtained for the^{234, 238}U targets and evidence for second order effects in the direct reaction mechanism was found.     

Study of the 182W(t,p)184W reaction at 20 MeV

The ¹⁸²W(t, p)¹⁸⁴W reaction has been studied at 20 MeV. The outgoing protons were detected in an Elbek broad range magnetic spectrograph. Absolute cross sections and angular distributions were measured. Evidence for inelastic effects in the reaction mechanism was observed for the first excited 2⁺ state, the 3^? level at 1221 keV and the 5⁺ state at 1295 keV. The 0⁺ level at 1002 keV was populated with ≈ 2% the ground state cross section. A 4⁺ level at 1536 keV was observed with ≈ 50% the ground state cross section. Calculations of the absolute (t, p) cross sections to this and other states with known structure resulted in excellent agreement with the measured values.     

Structure of 74Ge from the 72Ge(t,p) reaction

The reaction ⁷²Ge(t, p)⁷⁴Ge has been investigated with a 15 MeV triton beam. Fifty energy levels of ⁷⁴Ge were identified up to about 4.9 MeV excitation, eighteen of which were previously unreported. Angular distributions were measured and compared with DWBA calculations. Two low-lying states at 1.913 and 2.164 MeV have been assigned as J^π = 0⁺, corresponding to the 0₃⁺ and 0₄⁺ states in ⁷⁴Ge. The 4₂⁺ state has been located at 2.674 MeV, and the 2₄⁺ at 2.836 MeV. Many additional spin and parity assignments have been made. The ⁷⁴Ge nucleus shows a considerably different structure of 0⁺ states compared with the neighboring ⁷⁶Ge and ⁷⁸Ge nuclei, perhaps further evidence for the shape transition suggested recently for the Ge isotopes.     

Nuclear structure studies in the tellurium isotopes: the Te(d, p)Te reaction

The levels of ¹²⁷Te have been studied with the ¹²⁶Te(d, p)¹²⁷Te reaction at 7.5 MeV bombarding energy using the MIT multiple-gap broad-range magnetic spectrograph. A total number of 154 levels was observed below 5.7 MeV excitation energy. The angular distributions of 47 of the emitted proton groups were compared with DWBA stripping calculations to determine the orbital angular momentum of the captured neutrons. Transition strengths (2J+1)S_{ln, j} were extracted and compared to pairing-theory calculations. The total number of vacancies measured in the and states in the target is 6.0 , which is considerably lower than the expected value of 7.4 from pairing theory. It is suggested that this discrepancy results mainly from failure of the DWBA theory to predict the correct cross section for the l_n = 5 transition.     

The (p,n) reaction on cadmium isotopes leading to the ground- and excited-state analogs

The (p, n) reactions to ground- and excited-state analogs on ^110,114,116Cd have been studied at a bombarding energy of 25 MeV. Angular distributions of emitted neutrons leading to ground-state analogs, and 2⁺, 3^? and 4⁺ excited-state analogs were obtained for each target. Angular distributions of differential cross sections to the ground-state analog agree with the predictions obtained from macroscopic DWBA calculations in which a Lane potential is employed. Coupled-channel calculations indicate the importance of two-step processes in the (p, n) transition to an excited-state analog. Further, the calculation using a larger value for the deformation parameter of the isovector part than of the isoscalar one fairly well describes the 2⁺ excited-state analog.     

Comparative spectroscopy with the (d, τ) reaction on even Ar isotopes

The (d, τ) proton pick-up reactions on ³⁶Ar and ³⁸Ar have been studied at an incident energy of 52 MeV. Differential cross sections were measured and spectroscopic factors were extracted for transitions to 14 states of ³⁵Cl and 13 states of ³⁷Cl, respectively. Many new $\text{5}\text{2}$⁺ states and nearly the complete $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength have been observed in both nuclei. The width of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ spectral distribution is appreciably smaller for the semi-closed shell nucleus ³⁸Ar than for ³⁶Ar and ⁴⁰Ar. The results are compared with those from the ⁴⁰Ar(d, τ) reaction and proton stripping reactions on each of the three argon isotopes. Recent shell model calculations proved to be well suited to describe excitation energies as well as spectroscopic factors for the low-lying positiveparity states. Mirror relations were established for the nuclei ³⁵Ar and ³⁵Cl. In ³⁷Cl we succeeded in observing a weak component of a 1p proton hole state at a separation energy of only 18 MeV.     

Study of 31P with the 29Si(3He,p)31P reaction

The ²⁹Si(³He, p)³¹P reaction has been investigated at a bombarding energy of 15.0 MeV. Excitation energies and angular distributions were measured for 28 levels below 7.2 MeV in excitation. L-values were extracted from DWBA fits to the data. Angular distributions for the low-lying states were compared with DWBA curves calculated from Nilsson-model wave functions.     

Energy levels of 94Ru observed with the 96Ru(p,t) reaction

The level structure of the neutron-magic nucleus ⁹⁴Ru, up to an excitation energy of 4 MeV, has been studied by means of the (p, t) reaction. Particular emphasis was placed on a search for excited 0⁺ levels, none of which have been reported previously. Among new levels observed in this study are 0⁺ levels at 2.995, 3.615 and 3.770 MeV, and the 3^? octupole vibration at 2.965 MeV.     

(p,t) strengths in the Ga isotopes

The (p, t) reaction on the two stable Ga isotopes has been performed at 25 MeV, with 11 keV energy resolution. Levels up to 3.5 MeV in ⁶⁷Ga and 4.3 MeV in ⁶⁹Ga were measured. Differences observed between the distribution of the L = 2 (p, t) strength and the distribution of the B(E2)↑ strength may be explained by a mixed character of the $\text{7}\text{2}{}_2$^? level wave function. The distribution of the L = 0 strength indicates that the striking change in the ground-state structure shown between N = 40 and 42 already begins, although weakly, between N = 38 and 40.     

First excited 0+ states in the germanium isotopes via the Se(d, 6Li) reaction

A systematic study of the even-A germanium isotopes with mass 70 ≦ A ≦ 78 via the Se(d, ⁶Li) reaction has been performed at E_d = 45 MeV. The reaction products were momentum analysed and mass identified with a QMG/2 magnetic spectrograph and the accompanying focal-plane detector system. The main emphasis of this investigation was on the nature of the first excited 0⁺ states. The striking variation in strength from one isotope to the other already observed in the (p, t) reactions to the same final nuclei is also seen for the α-pickup reaction. Previously derived wave functions that assume the excited 0⁺₂ states to be pure proton configuration states can also account for the present results.     

The (d,t) and (d,t) reactions on 18O and the 1p spin-orbit splitting

The reactions ¹⁸O(d, t)¹⁷O and ¹⁸O(d, τ)¹⁷N have been investigated at ifE_{d = 52 MeV}. Energy spectra of tritons and τ particles have been measured up to excitation energies of 25 MeV in ¹⁷O and 12 MeV ¹⁷N, respectively, and spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From a comparison of the t-and τ-spectra the distribution of $\text{T =}\text{1}\text{2}\text{and}\text{3}\text{2}$ spectroscopic strengths in ¹⁷O could be deduced and analog relations between $\text{T =}\text{3}\text{2}$ states in ¹⁷N and ¹⁷O could be established. Nearly the total $\text{T =}\text{3}\text{2}$ strengths of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ shells and nearly the complete $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ shell have been found, whereas only one third of the $\text{T =}\text{1}\text{2}$ strength of the $\text{1}\text{p}\text{3}\text{2}$. Shell could be clearly identified. The observed centroid energies are understood from the different $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$$\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}\text{1)}$ and $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ effective residual interactions. This supports a strong isospin dependence of the 1p spin-orbit splitting.     

The t-dn vertex function and the (t,d) reaction

Estimates are made of the t-dn vertex function which is proportional to D², a multiplicative factor appearing in the differential cross section for (t, d) reactions at sub-Coulomb energies. The factor D² is calculated using various triton internal wave functions and also by using dispersion relations for d-n scattering. Calculations also are made of the ³He-dp vertex functions, as well as the factor D²₀ which appears in the differential cross sections at higher energies.