Neutron Hole States Research Articles

Neutron-hole states in 131Sn and spin-orbit splitting in neutron-rich nuclei

In atomic nuclei, the spin-orbit interaction originates from the coupling of the orbital motion of a nucleon with its intrinsic spin. Recent experimental and theoretical works have suggested a weakening of the spin-orbit interaction in neutron-rich nuclei far from stability. To study this phenomenon, we have investigated the spin-orbit energy splittings of single-hole and single-particle valence neutron orbits of 132Sn. The spectroscopic strength of single-hole states in 131Sn was determined from the measured differential cross sections of the tritons from the neutron-removing 132Sn(d, t)131Sn reaction, which was studied in inverse kinematics at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. The spectroscopic factors of the lowest 3/2+, 1/2+ and 5/2+ states were found to be consistent with their maximal values of (2j+1), confirming the robust N=82 shell closure at 132Sn. We compared the spin-orbit splitting of neutron single-hole states in 131Sn to those of single-particle states in 133Sn determined in a recent measurement of the 132Sn(d, p)133Sn reaction. We found a significant reduction of the energy splitting of the weakly bound 3p orbits compared to the well-bound 2d orbits, and that all the observed energy splittings can be reproduced remarkably well by calculations using a one-body spin-orbit interaction and a Woods–Saxon potential of standard radius and diffuseness. The observed reduction of spin-orbit splitting can be explained by the extended radial wavefunctions of the weakly bound orbits, without invoking a weakening of the spin-orbit strength.

Unexpected distribution of ν1f7/2 strength in Ca49

The calcium isotopes have emerged as a critical testing ground for new microscopically derived shell-model interactions, and a great deal of experimental and theoretical focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with 1f7/2 neutron hole states in Ca47,49 following one-neutron knockout reactions from Ca48,50. The observed reduction of strength populating the 7/21- state in Ca49, as compared to Ca47, is inconsistent with shell-model calculations using both phenomenological interactions such as GXPF1, and interactions derived from microscopically based two- and three-nucleon forces. The result suggests a fragmentation of the l=3 strength to higher-lying states as suggested by the microscopic calculations, but the observed magnitude of the reduction is not reproduced in any shell-model description.

Formation of Deeply Bound Pionic Atoms and Pion Properties in Nuclei

We study theoretically the formation of the deeply bound pionic atoms in various cases to deduce the pion properties in nuclei precisely from the observables. We show the angular dependence of the pionic atom formation spectra of the 122 Sn(d, 3 He) reactions in the forward angles. At each scattering angle, a different combination of the pion-bound and neutron-hole states dominates the spectrum because of the kinematical condition. We conclude that we can obtain information on the deeply bound pionic 2p state in addition to the 1s and 2s states by observing the spectra in finite angles. We also consider the neutron-odd nucleus as a target nucleus of the formation reaction, because it has an advantage that the pionic atom is formed in the even-even nucleus, of which the ground state has no neutron-hole states. In the 117 Sn(d; 3 He) reaction, we find that we can see clearly the peak structure of the pionic 1s state formation with the ground state of the even-even nucleus 116 Sn. The pionic atom in the even-even nucleus will not have additional shifts induced by the effects of the residual interaction between pion-bound and neutron-hole states. The observation of these pionic states is preferable for extracting the accurate information on the pion properties from data.

Neutron-hole states in45Ar from1H(46Ar, d) 45Ar reactions

To improve the effective interactions in the $pf$ shell, it is important to measure the single-particle and single-hole states near the $N$ $=$ 28 shell gap. In this paper, the neutron spectroscopic factors of hole states from the unstable neutron-rich ${}^{45}$Ar ($Z$ $=$ 18,$N$ $=$ 27) nucleus have been studied using the ${}^{1}$H(${}^{46}$Ar,$d$) ${}^{45}$Ar transfer reaction in inverse kinematics. Comparison of our results with the particle states of ${}^{45}$Ar produced in ${}^{2}$H(${}^{44}$Ar, $p$) ${}^{45}$Ar reaction shows that the two reactions populate states with different angular momenta. Using the angular distributions, we are able to confirm the spin assignments of four low-lying states of ${}^{45}$Ar. These are the ground state (${f}_{7/2}$), the first-excited state (${p}_{3/2}$), and the ${s}_{1/2}$ and ${d}_{3/2}$ states. While large basis shell-model predictions describe spectroscopic properties of the ground and ${p}_{3/2}$ states very well, they fail to describe the ${s}_{1/2}$ and ${d}_{3/2}$ hole states.

(d,3He) reaction on an odd-neutron nuclear target for the formation of deeply bound pionic atoms

We consider the pionic atom spectroscopy by the (d,3He) reaction on an odd-neutron nuclear target in this article, which has not been investigated so far. In the (d,3He) reaction on the odd-neutron nuclear target, we can observe the pionic states in the even-neutron nucleus with spin-parity 0+. We expect that this pionic state does not have the additional shifts due to the effects of the residual interaction between neutron-hole and pionic states. For the even-neutron nuclear target cases, we may have to take into account the residual interaction effects to deduce the binding energies of the pionic states precisely from the high precision experimental data since the final pionic states are the pion-particle plus neutron-hole states. Thus, in addition to widening the domain of the pionic atom spectroscopy in nuclear chart, the present study of the (d,3He) reaction on the odd-neutron target is considered to be important to deduce extremely precise information on the binding energies of the observed pionic states, and to know the pion properties and aspects of the symmetries of the strong interaction at finite density. We modify the formula of the even-even nuclear target case to study the pionic atom formation spectra on the even-odd nuclear target and show the numerical results of 117Sn target case. This experiment will be performed at RIBF/RIKEN in near future.

Formation of deeply bound pionic atoms in Sn isotopes

We study the formation of deeply bound pionic atoms in the (d ,3 He) reactions theoretically and show the energy spectra of the emitted 3 He at finite angles. We find that the different combinations of the pion-bound and neutron-hole states dominate the formation spectra at different scattering angles because of the matching condition of the reaction. We conclude that the observation of the (d ,3 He) reaction at finite angles will provide the systematic information of the pionic bound states in each nucleus, and it will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.

Pionic atom spectroscopy in the (d,3 He) reaction at finite angles

We study the formation of deeply bound pionic atoms in the (d,3He) reactions theoretically and show the energy spectra of the emitted 3He at finite angles, which are expected to be observed experimentally. We find that the different combinations of the pion-bound and neutron-hole states dominate the spectra at different scattering angles because of the matching condition of the reaction. We conclude that the observation of the (d,3He) reaction at finite angles will provide the systematic information of the pionic bound states in each nucleus and will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.

Rotational and neutron-hole states inS43via the neutron knockout and fragmentation reactions

The recent assertion that shape coexistence occurs in the neutron-rich isotope $^{43}\mathrm{S}$ implies that a state observed at 940 keV in a previous study is a rotational excitation of the deformed ground state. Here we use results from two intermediate-energy reactions to demonstrate that this state---assigned an energy of 971 keV in the present work---is indeed a rotational state. This result strengthens the case for shape coexistence in $^{43}\mathrm{S}$.

Selectivity of the one-neutron knockout reaction onCl45and the collapse of theN=28shell closure

Neutron hole states in the exotic $N=27$ isotope $^{44}\mathrm{Cl}$ have been populated using the intermediate-energy single-neutron knockout reaction $^{9}\mathrm{Be}(^{45}\mathrm{Cl},^{44}\mathrm{Cl})\mathrm{X}$. The momentum distribution of the residual $^{44}\mathrm{Cl}$ nuclei after direct population of the ground state is consistent with removal of an $l=1$ neutron. This observation and comparison with a shell-model calculation imply that ${p}_{3/2}$ neutrons from above the $N=28$ major shell closure play important roles in the ground states of both $^{44}\mathrm{Cl}$ and $^{45}\mathrm{Cl}$. The present result is significant because $^{44}\mathrm{Cl}$ is even closer to the valley of stability than $^{43}\mathrm{S}$, where a similar result was recently obtained using a $g$-factor measurement.

Intermediate energy proton knockout to the “island of inversion” isotopeMg31

The ``island of the inversion'' isotope $^{31}\mathrm{Mg}$ was investigated using an intermediate energy proton knockout reaction from $^{32}\mathrm{Al}$ at 90 MeV/nucleon at the National Superconducting Cyclotron Laboratory. A negligible cross section to the ground state supports an intruder-dominant configuration in $^{31}\mathrm{Mg}$. The partial cross sections to excited final states preferentially populate configurations in the $^{31}\mathrm{Mg}$ residues which have no neutron excitations across the $N=20$ shell closure. There is strong evidence that the reaction populates the $3/{2}^{+}$ and $5/{2}^{+}$ states which correspond with the neutron-hole states predicted by the shell model with the model space truncated above the $\mathit{sd}$-shell.

MICROSCOPIC STRUCTURE OF THE DIPOLE COMPRESSION MODE IN HEAVY NUCLEI

Neutron decay of the isoscalar giant dipole resonance (ISGDR) has been studied in90Zr ,116Sn and208Pb using the (α,α′) reaction at a bombarding energy of 200 MeV. The same reaction was used to study proton decay of the ISGDR in58Ni and208Pb . Neutron and proton decay of the ISGDR to low-lying neutron and proton hole states in the daughter nuclei, respectively, allowed an experimental determination of the ISGDR microscopic structures. The determined branching ratios are compared to recent continuum random-phase-approximation (CRPA) calculations. Reasonable agreement was observed for208Pb and58Ni , whereas strong differences for90Zr and116Sn were found.

Decays ofIn131,Sn131, and the position of theh11∕2neutron hole state

The decays of the three isomers of $^{131}\mathrm{In}$ and the total decay energies of the two isomers of $^{131}\mathrm{Sn}$ have been studied in high sensitivity experiments at the OSIRIS mass separator. The main purpose of the investigation was to determine the position of the neutron hole ${h}_{11∕2}$ state, since a previous determination appeared to be in error. The present results support a small separation of the ${d}_{3∕2}$ and ${h}_{11∕2}$ neutron hole states. The new value obtained from measurements of decay energies is $69\ifmmode\pm\else\textpm\fi{}14\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. A more precise value of $65.1\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ may be deduced from the level scheme of $^{131}\mathrm{Sn}$ obtained currently, however without firm support from coincidence data. This relatively low excitation energy of the ${h}_{11∕2}$ state is in agreement with systematics and in disagreement with the previous determination. A re-evaluation of the ${Q}_{\ensuremath{\beta}}$ values and isomer spacings of $^{131}\mathrm{In}$ has been made.

Particle decay of the isoscalar giant dipole resonance inPb

The direct particle decay of the isoscalar giant dipole resonance (ISGDR) has been studied in208Pb using the (α, α′p) and (α, α′n) reactions at a bombarding energy of 200 MeV. The direct-decay channels of proton and neutron emissions were observed in coincidence with the scattered α-particles in order to study the population of proton-hole states in207T1 and neutron-hole states in207Pb. The results of the partial and total branching ratios allowed us to test recently performed continuum-RPA (CRPA) calculations for the ISGDR and thereby to learn about its microscopic structure.

Particle decay of the isoscalar giant dipole resonance inPb

The direct particle decay of the isoscalar giant dipole resonance (ISGDR) has been studied in208Pb using the (α, α′p) and (α, α′n) reactions at a bombarding energy of 200 MeV. The direct-decay channels of proton and neutron emissions were observed in coincidence with the scattered α-particles in order to study the population of proton-hole states in207T1 and neutron-hole states in207Pb. The results of the partial and total branching ratios allowed us to test recently performed continuum-RPA (CRPA) calculations for the ISGDR and thereby to learn about its microscopic structure.

Particle decay of the isoscalar giant dipole resonance in 208Pb

The direct particle decay of the isoscalar giant dipole resonance (ISGDR) has been studied in 208Pb using the (α, α′ p) and (α, α′ n) reactions at a bombarding energy of 200 MeV. The direct-decay channels of proton and neutron emissions were observed in coincidence with the scattered α-particles in order to study the population of proton-hole states in 207T1 and neutron-hole states in 207Pb. The results of the partial and total branching ratios allowed us to test recently performed continuum-RPA (CRPA) calculations for the ISGDR and thereby to learn about its microscopic structure.

Microscopic structure of the Gamow-Teller resonance inCu58

The Gamow-Teller (GT) states in $^{58}\mathrm{Cu}$ have been studied via the $^{58}\mathrm{Ni}(^{3}\mathrm{He},t+p)$ and $^{58}\mathrm{Ni}(^{3}\mathrm{He},t+\ensuremath{\gamma})$ coincidence experiments. The GT states in $^{58}\mathrm{Cu}$ at ${E}_{x}=6--12\phantom{\rule{0.3em}{0ex}}\text{MeV}$, where both $T=1$ and $T=2,{1}^{+}$ states exist, are excited strongly in the $^{58}\mathrm{Ni}(^{3}\mathrm{He},t)$ reaction at $E(^{3}\mathrm{He})=450\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$. Proton emissions from the GT states in $^{58}\mathrm{Cu}$ to the hole states in $^{57}\mathrm{Ni}$ have been observed with solid-state detectors in coincidence with high energy tritons measured with a magnetic spectrometer. For the first time, the $\ensuremath{\gamma}$-ray emissions from the excited states in $^{58}\mathrm{Cu}$ and in $^{57}\mathrm{Ni}$, following the $^{58}\mathrm{Ni}(^{3}\mathrm{He},t+p)$ reaction at intermediate energies, have also been observed in coincidence with tritons. Strengths of proton decay into several neutron-hole states in $^{57}\mathrm{Ni}$ and $\ensuremath{\gamma}$-decay strengths are used to discuss the wave functions of the GT states in $^{58}\mathrm{Cu}$. The $T=1$ and $T=2$ GT states do only weakly decay into a $T=3∕2,{f}_{7∕2}^{\ensuremath{-}1}$ neutron-hole state at $5.230\phantom{\rule{0.3em}{0ex}}\text{MeV}$ in $^{57}\mathrm{Ni}$, which is strongly excited via the $^{58}\mathrm{Ni}(p,d)^{57}\mathrm{Ni}$ reaction. The wave functions of the $T=1$ and $T=2$ GT states with the ${f}_{7∕2}^{\ensuremath{-}1}$ neutron-hole configuration are inferred to be strongly coupled to $2p\text{\ensuremath{-}}2h$ configurations, making fragmented GT strengths in $^{58}\mathrm{Cu}$.

Excitation and decay of the isovector giant monopole resonances via the 208Pb(3He,t p) reaction at 410 MeV.

The excitation and subsequent proton decay of the isovector spin-flip giant monopole resonance (IVSGMR) is studied via the 208Pb(3He,t) reaction at 410 MeV. In the inclusive spectrum (60+/-5)% of the non-energy-weighted sum-rule strength for this 2 variant Planck's over 2h omega resonance was found in the region 29<Ex(208Bi)<51 MeV. The central excitation energy and width of the IVSGMR are 37+/-1 MeV and 14+/-3 MeV, respectively. It is found that the branching ratio for proton decay is (52+/-12)% and that the deep neutron-hole states in 207Pb are strongly fed.

100Mo( [formula omitted]) 99Mo reaction at 21 MeV and direct reaction analysis of the low-lying continuum spectrum

The 100Mo( p → ,d ) 99Mo reaction has been studied with 21 MeV polarized protons. Momentum spectra of the emitted deuterons corresponding to the excitation energy region up to 5.75 MeV in 99Mo have been measured. Theoretical analysis based on the standard distorted-wave Born approximation (DWBA) provides the lj-angular momentum transfers and spectroscopic factors of neutron hole states for 27 levels from the ground state up to E X =2.921 MeV. The polarization data gave a more affirmative information in assigning the spins and parities. Spectrum regions from discrete levels to continuum were treated with a global analysis using the direct reaction model and continuous strength functions. The double differential cross section-energy spectra were reproduced fairly well using the DWBA-based cross sections and the asymmetrical Lorentzian form strength response function having energy-dependent spreading widths.

One-neutron transfer reaction and refractive effects in the 16O+ 16O system

One-neutron transfer data of the 16O( 16O, 17O) 15O reaction have been measured for the p 1/2 ground state and p 3/2 excited hole state in 15O, at incident energies ranging from 250 to 1120 MeV. Some remnant of refraction (rainbow) pattern was observed for the ground state transition to 15O 1/2 − , whereas for the neutron hole state 15O ∗ 3/2 − at 6.176 MeV excitation energy the angular distributions show more or less an exponential fall-off. The data were analyzed using the full finite-range distorted wave Born approximation (DWBA). The DWBA description of the transfer data over the whole measured angular range was possible only, if the indirect term of the transition operator is properly included and the absorption in the exit channels is substantially increased, especially, for the 15O ∗ 3/2 − channel. The energy dependence of the transfer cross sections has been consistently described with two choices for the real part of the optical potential: the folding potential and the squared Woods–Saxon potential. The obtained spectroscopic factors, S(1/2 −)=1.8±0.3 and S(3/2 −)=4.0±0.5, are energy independent.

Zero-energy π−–D scattering: precise determination of the πN scattering lengths and of the charged coupling constant

The recent progress in the study of the pion–nucleus s-wave interaction by the discovery of discrete excited states below the pion threshold in heavy nuclei is reviewed. These states are populated by ( d, 3He ) reactions at bombarding energies of 500–600 MeV, with the 3He observed at forward direction under kinematic conditions, where a large energy (in the order of a pion mass), but only a small momentum is transferred (recoil-free). The resulting distinct pattern of states can be uniquely assigned to deeply bound π− states coupled to well known neutron–hole states with the configurations (nl)π(n′l′j)n−1. With sufficient energy resolution in the ( d, 3He ) spectroscopy it was for the first time possible to determine the excitation energy of each configuration with respect to the ground state of the residual nucleus with A−1 and from this also the binding energy, Bnl, and even the natural width, Γnl, of the pionic state.A summary of the results on binding energies and widths of pionic 1s and 2p states in nuclei with large neutron excesses, such as 207Pb, 205Pb, 123Sn, 119Sn and 115Sn is given. The structure of these states is determined by a superposition of a large repulsive s-wave π−–nucleus interaction and an attractive Coulomb interaction, such that the pions are bound in a potential pocket at the surface of the nuclei, which leads to a halo-like pion distribution around the nucleus. The repulsive s-wave interaction reduces the binding energies of the 1s states in the Pb nuclei by roughly a factor of two and the widths to about 760 keV, which makes them discrete with no overlap to other states. The pion–nucleus interaction has its maximum contribution from an effective density ρe≈0.6ρ0. So it is a sensitive tool to test in-medium effects by comparison with the known s-wave pion–nucleon interaction. An empirical procedure is developed to derive the s-wave pion nucleus potential parameters unambiguously by using only 1s-state binding energies and widths of pionic atoms of light N=Z nuclei as well as of deeply bound pionic 1s states of heavy nuclei with large neutron excesses. The isovector s-wave parameter was deduced as b1=−0.115±0.007mπ−1, which is found to be enhanced over the free πN scattering length (−0.090mπ−1). This result indicates that the order parameter of chiral symmetry breaking, fπ∗(ρ0)2, is reduced by a factor of ∼0.64 in a nucleus with density ρ0=0.17 fm. We also obtained the scaling parameter for the density dependence of the isovector pion–nucleus interaction strength to αρ0∼0.36 in good agreement with theoretical expectations. Thus we find clear evidence for partial chiral symmetry restoration in a nuclear medium.