Proton-hole States Research Articles

Proton-hole excitations in 201, 203Au from [formula omitted]) reactions

The 202, 204 Hg( t, α ) reactions have been performed to investigate the proton-hole states of 201, 203Au, for which no knowledge of the level structures was previously available. The results yield ground-state masses and locate a number of excited states below 2.5 MeV in each nuclide. Spins and parities of these levels can be assigned from angular distributions of the analyzing powers and differential cross sections, with the latter also being used to determine spectroscopic strengths. The results indicate a rather rapid fragmentation of single-proton strength as one goes away from the Z=82 closed shell, indicating a more collective structure.

Proton hole states in neutron rich nuclei nearA=100

A study of proton hole states in neutron rich nuclei near $A=100$ has been carried out using the ($\stackrel{\ensuremath{\rightarrow}}{t}$,$\ensuremath{\alpha}$) reaction. Targets of $^{104}\mathrm{Ru}$ and $^{110}\mathrm{Pd}$ were bombarded with a beam of 17 MeV polarized tritons and the reaction $\ensuremath{\alpha}$ particles detected in a quadrupole-three-dipole spectrometer. Only the $\ensuremath{\beta}$ decays of the residual nuclei, $^{103}\mathrm{Tc}$ and $^{109}\mathrm{Rh}$, have been previously observed. The results indicate a smooth trend with $Z$ of the proton single particle states observed in this region, except for $^{103}\mathrm{Tc}$. Examination of this nucleus indicates a strong tendency towards deformation.

Ca40(d,He3)K39reaction at 76 MeV

The differential cross sections of the $^{3}\mathrm{He}$ groups emitted in the $^{40}\mathrm{Ca}(d,^{3}\mathrm{He})^{39}\mathrm{K}$ reaction have been measured at a bombarding energy of 76 MeV. The $^{3}\mathrm{He}$ particles were measured with an energy resolution of 55 keV. Differential cross sections were fitted using a distorted wave program and spectroscopic factors were deduced for several proton hole states of $^{39}\mathrm{K}$. The single hole final states essentially exhaust the sum rule for the $1{d}_{\frac{3}{2}}$, $2{s}_{\frac{1}{2}}$, and $1{d}_{\frac{5}{2}}$ subshells. Because of the strong absorption of $^{3}\mathrm{He}$ particles in nuclear matter, this reaction is a surface reaction, and as such populates only the outer shells. By contrast, the $^{40}\mathrm{Ca}(p,2p)$ reaction is able to populate all proton hole states, including those of the $1p$ and $1s$ shells. The population of the quartet of odd parity states, which from a nuclear structure point of view consist of a ${1d}_{\frac{3}{2}}$ hole coupled to the ${3}^{\ensuremath{-}}$ state of $^{40}\mathrm{Ca}$, was observed. The differential cross sections for the $^{3}\mathrm{He}$ groups populating those states were calculated using a coupled channels program and these calculations are in satisfactory agreement with the experimental results.[NUCLEAR REACTIONS $^{40}\mathrm{Ca}(d,^{3}\mathrm{He})$, $E=76$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, enriched target. DWBA and CCBA analysis, deduced spectroscopic factors.]

Analyzing powers for the (p, α) reactions on 58, 60, 62Ni at Ep = 22 MeV

Measurements of both the analyzing power and cross section were made for the (p, α) reactions on 58,60,62Ni at an incident energy of 22 MeV. Data were taken for the strongly populated proton-hole states (0f 7 2 , 1s 1 2 and 0d 3 2 ) in the residual cobalt isotopes and for 8 weakly populated low-lying states in 55Co and 59Co. Angular distributions were taken between θ lab = 10° and 140° for the ground state and θ lab = 10° and 80° for the excited states. Both the cross sections and analyzing powers exhibit a similar angular distribution for states having the same J π values except in the transition to the 3 2 − state in 59Co at 1.099 MeV. Using the observed J-dependence of the analyzing power, the unknown J π values for the states at 2.982 MeV in 55Co and 3.090 MeV in 59Co are assigned to be 9 2 −. The shapes of the differential cross sections were well reproduced by the zero-range DWBA calculations using a triton-cluster form factor. However, all the measured analyzing powers could not be reproduced within the framework of such a simple DWBA calculation.

High-spin states in odd-massSb113−119:ΔJ=1bands on92+proton-hole states

Properties of high-spin states in $^{113,115,117,119}\mathrm{Sb}$ have been studied via the $^{A}\mathrm{Cd}(^{6}\mathrm{Li},3n)^{A+3}\mathrm{Sb}$ reactions. Using Ge(Li) and Si(Li) detectors, in-beam measurements of $\ensuremath{\gamma}$-ray excitation functions, $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}$-ray angular distributions, and pulsed beam-$\ensuremath{\gamma}$ timing spectra were made to determine level energies, decay schemes, $\ensuremath{\gamma}$-ray multipolarities, ${J}^{\ensuremath{\pi}}$ assignments, isomeric lifetimes, and a $g$ factor. Systematic $\ensuremath{\Delta}J=1$ bands built on low-lying $\frac{9}{{2}^{+}}$ proton-hole (2p-1h) states were observed in these nuclei. The bandheads that involve the excitation of a $1{g}_{\frac{9}{2}}$ proton across the $Z=50$ shell achieve an energy minimum near the middle of the neutron shell. The observed properties of these bands are consistent with significant prolate deformations; the band spacings imply a deformation asymmetry of $\ensuremath{\gamma}=20$ in a triaxial rotor model. In addition, single-particle and single-particle plus core-excitation states were observed in these Sb nuclei. Two isomers were identified, a $\frac{19}{{2}^{(\ensuremath{-})}}$ state at 2796 keV in $^{115}\mathrm{Sb}$ ($\ensuremath{\tau}=230\ifmmode\pm\else\textpm\fi{}4$ ns and $g=+0.290\ifmmode\pm\else\textpm\fi{}0.005$) and a ($\frac{27}{{2}^{+}}$) state in $^{119}\mathrm{Sb}$ ($\ensuremath{\tau}=1.23\ifmmode\pm\else\textpm\fi{}0.13$ s).NUCLEAR REACTIONS $^{110\ensuremath{-}116}\mathrm{Cd}$ ($^{6}\mathrm{Li}$,$3n$)$^{113\ensuremath{-}119}\mathrm{Sb}$; measured $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}(E,\ensuremath{\theta},t)$, spin rotation in $B=10.3$ kG; deduced level schemes in odd-mass $^{113\ensuremath{-}119}\mathrm{Sb}$, $\ensuremath{\gamma}$ multipolarities, ${J}^{\ensuremath{\pi}}$, ${T}_{\frac{1}{2}}$, $g$-factor. Enriched targets, Ge(Li) detectors.

Strong exhaustion of [formula omitted] strength by deeply-bound proton-hole states in Pm isotopes

The 1 g 9 2 proton-hole strength distributions in Pm isotopes have been investigated by the 144, 148, 152 Sm (d,τ) reactions at 52 MeV. Other than for corresponding neutron-hole states most of the shell-model strength is exhausted by one gross structure peak.

The 58, 60, 62, 64Ni(p, α) 55, 57, 59, 61Co reactions and their description by the semi-microscopic model for three-nucleon transfer

The (p, α) reaction on the even- A nickel isotopes has been studied at an incident proton energy of 30 MeV. Between 14 and 26 states, or groups of states, were analysed for each of the residual cobalt isotopes. For these transitions angular distributions were determined from θ lab = 7.5° to 70°. In all reactions the proton-hole states (0 f 7 2 , 1 s 1 2 and 0 d 3 2 ) stand out in the spectra. Also, states formed by the weak-coupling of the proton-holes to excitations of the neutron core were seen. Differences in the relative strengths of the positive-parity hole states between the proton pickup and the (p, α) data can be explained by a semi-microscopic model for three-nucleon transfer. Also the strength distribution of the transitions to the lowest weak-coupling quintuplet is correctly predicted. These results underline the importance of the inclusion of non-zero coupled neutron pairs into the description of (p, α) reactions. Several T > states are observed in the 58Ni(p, α) 55Co reaction.

Cr52(p, α)V49reaction

The $^{52}\mathrm{Cr}(p, \ensuremath{\alpha})^{49}\mathrm{V}$ reaction has been studied at a bombarding energy of 35 MeV. The qualitative features of the spectra are discussed. These include the population of proton hole states, analog states, and high spin states. The spectra are compared with other pick-up reaction data and the comparison is shown to be a useful tool for identifying positive parity states in this region. Some states which are observed in $^{51}\mathrm{V}(p, t)^{49}\mathrm{V}$ data are not observed in the ($p, \ensuremath{\alpha}$) spectra. Distorted-wave calculations using mass three cluster form factors are described and shown to reproduce the experimental angular distributiions of the previously known levels. Similar calculations using microscopic form factors also reproduce the shapes of the angular distributions reasonably well. Relative spectroscopic factors for the proton hole states deduced from the microscopic calculations are shown to be in good agreement with zero order shell model predictions. The general trends of the experimental cross sections for the negative parity microscopic states are shown to be reproduced by microscopic calculations assuming $0{{f}_{\frac{7}{2}}}^{3}$ pickup.NUCLEAR REACTIONS $^{52}\mathrm{Cr}(p, \ensuremath{\alpha})$, ${E}_{p}=35$ MeV; measured $\ensuremath{\sigma}({E}_{x}\ensuremath{\theta})$, deduced energy levels; studied reaction mechanism.

Ni58(p, α)Co55reaction and levels ofCo55

The $^{58}\mathrm{Ni}(p, \ensuremath{\alpha})^{55}\mathrm{Co}$ reaction was used to measure both direct and compound cross sections for nuclear levels in $^{55}\mathrm{Co}$. The primary proton hole strengths are in the ground ($1{f}_{\frac{7}{2}}$), 2919-keV ($2{s}_{\frac{1}{2}}$), and 3563-keV ($1{d}_{\frac{3}{2}}$) states whose energies agree well with those predicted by systematics. Cross sections for the same hole states were also measured in $^{57,59,61}\mathrm{Co}$. A Hauser-Feshbach calculation indicates significant deviation from the ($2J+1$) rule for compound nuclear states. The largest cross section occurs for $J=\frac{7}{2}$ states. Thus states with larger experimental cross sections can be identified as doublets, e.g., the 2919- and 2974-keV states.NUCLEAR REACTIONS $^{58,60,62,64}\mathrm{Ni}(p, \ensuremath{\alpha})$, $E=15\ensuremath{-}17$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$. Identified proton hole states, DWBA analysis. Hauser-Feshbach analysis. Enriched targets.

Deformed92+Proton-Hole States on Odd-ACs119−125

..delta..J = 1 bands built on deformed 9/2/sup +/ proton-hole states have been observed in /sup 119 -125/Cs. The 9/2/sup +/ bandhead energies drop phenomenally to become the ground state in /sup 119/Cs(N = 64). The band systematics for N(62-74) and Z(51-55) are defined. A deformed-structure relationship is suggested between the excitations of 1g/sub 9/2/ proton and a pair of 1g/sub 9/2/ proton across the Z = 50 closed shell.

Spins of proton hole states from analyzing powers of (d, τ) reactions at 52 MeV

Large and characteristic vector-analyzing powers of the ( d , τ) reactions on 16O, 28Si and 40Ca at 52 MeV have been observed and utilized to determine the spins of 1p hole states in 15N and 27Al and of 1d hole states in 39K. The results are pertinent to the empirical determination of the 1p and 1d spin-orbit splittings.

Proton hole states in 114Cd excited in the 115In(d, 3He) 114Cd reaction at Ed = 50 MeV

The 115In(d, 3He) 114Cd reaction was studied at E d = 50 MeV. For transitions to states in 114Cd in the excitation energy range 0–5.3 MeV angular distributions were obtained, most of them corresponding to l p = 1(2 p 1 2 , 2 p 3 2 ) or l p = 4(1g 9 2 ) transfer. From DWBA analysis spectroscopic factors were extracted and compared with sum rules. An 8 +state at 3.25 MeV is proposed. A comparison with semi-microscopic model calculations is made.

Neutron-hole strengths and isobaric analog states in 95Zr

The 96Zr(τ, α) 95Zr reaction at 39 MeV incident energy was used to populate both the low-lying and highly excited (up to an excitation energy of 18 MeV) analog states in 95Zr and some low-lying levels in other Zr isotopes. The main components of the 2d 5 2 . and 1g 9 2 . hole strengths and the analogs of the 2p 1 2 ., 2p 3 2 . and 1f 3 2 . proton hole states in 95Y have been observed in this work. Angular distributions of transitions to 27 levels in 95Zr have been extracted and analysed with DWBA calculations to yield spectroscopic factors. Between the excitation energies of 1 and 3 MeV in 95Zr a number of levels with l = 2, 4 and 5 angular distributions have been identified. These are associated with the 2d 3 2 , 1g 7 2 and 1h 11 2 components already observed in the previous study of the 94Zr(d, p) and (α, τ) reactions. The total strength and center of gravity for levels assigned to the (1g 9 2 ) −1 configurations in 95Zr are presented and compared to the results obtained from the studies of neutron pick-up reaction on 91Zr and 98Mo. For the isobaric analog states observed between the excitation energies of 15 and 17 MeV, total widths, Coulomb displacement energies and spectroscopic factors are also determined from this experiment and the results compared with the properties of the low-lying proton hole states in the 95Y parent nucleus.

Proton hole states in 187, 189, 191Re investigated by the ( [formula omitted]) reaction

Proton hole states in 187Re, 189Re and 191Re have been studied using the ( t , α ) reaction. Beams of 17 MeV tritons with a polarization of 0.75 were obtained from the tandem Van de Graaff accelerator at the Los Alamos Scientific Laboratory. The α-particles were detected in a Q3D magnetic spectrometer with a helical-cathode position-sensitive proportional counter. Spectra were recorded up to > 2 MeV excitation energy with a resolution (FWHM) of ≈ 20 keV. These measurements exhibit large analyzing powers for transitions to well-known states in the deformed nuclide 187Re. This is of interest because the only other single-nucleon transfer results on heavy deformed nuclei (in a ( d, p ) study of tungsten isotopes) showed “disappointingly small” analyzing powers. The ( t ,α ) analyzing powers were reproduced by DWBA calculations very well. Thus other levels in 187Re and many states in 189Re and 191Re could be assigned spins and parities on the basis of angular distributions for the cross sections and analyzing powers. In particular, the present results have made it possible to determine which of the three possible interpretations suggested previously for the structure of 191Re is correct. The results have been interpreted within the framework of the Nilsson model, with pairing and Coriolis mixing corrections included. The energy systematics of single-quasiparticle states are well reproduced by the Nilsson model if a hexadecapole deformation is included in the nuclear potential. Finally, it has been demonstrated that the ( t , α ) reaction is an extremely useful spectroscopic tool for studies of heavy deformed nuclei.

Unified theory of particle-phonon coupling: Application to Sb and In isotopes using a realistic interaction

A self-consistent, unified, microscopic theory ofparticle-phonon coupling is applied to the Sb and In isotopes, which are treated as proton-particle and proton-hole states respectively coupled to the ground and low-lying vibrational states of Sn. The particle-phonon coupling interaction is derived from the same realistic two-body interaction which gives rise to the vibrational excitations in Sn. Spectroscopic factors, level schemes and B( E2) values calculated with no adjustable parameters are shown to be in good agreement with experimental data.

Deformed92+proton-hole states in odd-AI nuclei

$\ensuremath{\Delta}J=1$ bands built on low-lying $\frac{9}{{2}^{+}}$ states (307 keV in $^{119}\mathrm{I}$) have been observed in odd-$A$ $^{117.127}\mathrm{I}$ ($Z=53$) nuclei via ($^{6}\mathrm{Li}$, $3n\ensuremath{\gamma}$) reactions. Calculations of the total potential energy of these nuclear states in terms of a $[404]\frac{9}{{9}^{+}}$ Nilsson proton hole revealed minima at significant prolate deformations ($\ensuremath{\epsilon}=0.22$ for $^{119}\mathrm{I}$). The resulting excitation energies and band spacing calculations are in good agreement with experiment. The properties of these deformed $\frac{9}{{2}^{+}}$ states, which involve a $1{g}_{\frac{9}{2}}$ proton excited through the $Z=50$ major shell, are compared with those of the deformed $\frac{9}{{2}^{+}}$ states previously observed in odd-Sb ($Z=51$) nuclei.NUCLEAR REACTIONS $^{114\ensuremath{-}124}\mathrm{Sn}(^{6}\mathrm{Li}, 3n)$, ${E}_{\mathrm{Li}}=25\ensuremath{-}35$ MeV, measured $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences, $\ensuremath{\gamma}(E, \ensuremath{\theta}, t)$; deduced level scheme in odd-$A$ $^{117\ensuremath{-}127}\mathrm{I}$, $\ensuremath{\gamma}$ multipolarities, ${J}^{\ensuremath{\pi}}$. Enriched targets, Ge(Li) detectors.NUCLEAR STRUCTURE Odd-$A$ $^{117\ensuremath{-}127}\mathrm{I}$, calculated ${\frac{9}{2}}^{+}$ proton-hole state energies, $\ensuremath{\Delta}J=1$ rotational bands.

Spectroscopy of proton hole states in the thallium nuclei with the ( [formula omitted] reaction

Proton hole states are observed in 203,205,207Tl isotopes using the ( t, α) reaction. The study was made with a beam of tritons with 75 % polarization and with the reaction α-particles being detected in a Q3D spectrometer by a helix detector system. The 206 Pb( t, α) 207 Tl results serve as a template for the analyzing powers of the various transferred proton spins. Distorted wave calculations agree well with these results and are used to make Q and mass corrections. A number of spin assignments are made in 205Tl although the emphasis is on 203Tl where few spin assignments were previously available. The systematic trend of the proton hole energy centroids as a function of mass in the region Z = 82 is also presented.

Collective properties of A = 117−127 odd- A I nuclei

Systematic ΔJ = 2 bands have been observed on the d 5 2 , g 7 2 and h 11 2 quasi-proton states in A = 117−127 odd-I nuclei. The ΔJ = 2 energy spacings decrease (relative to the Te cores) as A decreases for the h 1 2 band but not for the others. Also ΔJ = 1 bands on unsually low-lying g 9 2 proton-hole states exist.

The 27Al, 40Ca and 51V(e, e′p) reactions and observation of deep hole states

Information on proton hole states has been obtained for 27Al, 40Ca and 51V through the (e, e'p) reaction. Lower-lying hole states have been identified. For 40Ca an extensive analysis has been performed to study the structure of the 1s hole state. For 27Al and 51V, the properties of the 1s hole states have also been determined. The separation energies of the 1p and 1s states seem to be constant (40 and 60 MeV, respectively) for A > 30.

Semi-microscopic description of three-nucleon transfer and the Sn(p, α)In reaction

Differential cross sections have been measured in the angular range from 10° to ≈ 60° for the 112, 116, 118, 124Sn(p, α) 109, 113, 115, 121In reaction at an incident energy of E p = 22 MeV. The 124Sn(p, α) 121In reaction also was studied at E p = 30 MeV. From the observed differences between the (p, α) and one-proton pickup data it is inferred that coherence effects play an important role arising from additional contributions to the reaction amplitude in which the picked-up neutrons do not form a zero-coupled pair. A semi-microscopic model has been developed to calculate relative transition strengths assuming a one-step pickup process for the (p, α) reaction. Detailed calculations were carried out for the 118Sn(p, α) 115In reaction by employing weak-coupling wave functions for 115In. The calculations account well for the observed differences between the one-proton pickup and the (p, α) data and correctly reproduce the relative intensities for the 0 g 9 2 , 1 p 1 2 and 1 p 3 2 proton-hole states and the |0 g 9 2 −1 ⊗2 +〉 weak-coupling multiplet. In addition to the reaction mechanism study new sctroscopic information was obtained for some of the odd-A indium isotopes.