Neutron Effective Charge Research Articles

Quadrupole dominance in the light Sn and in the Cd isotopes

[Background] The BE2 rates of the Sn isotopes for $N\le 64$ exhibit enhancements hitherto unexplained. The same is true for the Cd isotopes. [Purpose] Describe the electromagnetic properties of the Sn and Cd isotopes [Method] Shell model calculations with a minimally renormalized realistic interaction, supplemented by Quasi and Pseudo-SU3 symmetries and Nilsson-SU3 selfconsistent calculations. [Results for $N\le 64$] Shell model calculations with the neutron effective charge as single free parameter describe well the BE2(2>0) and BE2(4>2) rates for $N\le 64$ in the Cd and Sn isotopes. The former exhibit weak permanent deformation corroborating the prediction of a Pseudo-SU3 symmetry, which remains of heuristic value in the latter, where the pairing force erodes the quadrupole dominance. Calculations in $10^7$ and $10^{10}$-dimensional spaces exhibit almost identical patterns: A vindication of the shell model. [Results for $N\ge 64$] Nilsson-SU3 calculations describe BE2 patterns in [112-120]Cd and [116-118]Sn isotopes having sizable quadrupole moment of non-rotational origin denoted as q-vibrations. No calculations are proposed for the heavier species, for which the conventional seniority dscription is assumed for Sn, while in Cd the quadrupole moments change sign. [Conclusion] A radical reexamination of traditional interpretations in the region has been shown to be necessary, in which quadrupole dominance plays a major role. What emerges is a bumpy but coherent view.

Electric quadrupole moments of the21+states inCd100,102,104

Using the REX-ISOLDE facility at CERN the Coulomb excitation cross sections for the 0gs+→21+ transition in the β-unstable isotopes Cd100,102,104 have been measured for the first time. Two different targets were used, which allows for the first extraction of the static electric quadrupole moments Q(21+) in Cd102,104. In addition to the B(E2) values in Cd102,104, a first experimental limit for the B(E2) value in Cd100 is presented. The data was analyzed using the maximum likelihood method. The provided probability distributions impose a test for theoretical predictions of the static and dynamic moments. The data are interpreted within the shell-model using realistic matrix elements obtained from a G-matrix renormalized CD-Bonn interaction. In view of recent results for the light Sn isotopes the data are discussed in the context of a renormalization of the neutron effective charge. This study is the first to use the reorientation effect for post-accelerated short-lived radioactive isotopes to simultaneously determine the B(E2) and the Q(21+) values.4 MoreReceived 20 May 2009DOI:https://doi.org/10.1103/PhysRevC.80.054302©2009 American Physical Society

Decoupling of valence neutrons from the core in 17B

Proton inelastic scattering study of 17B nucleus has been performed at 43.8 A MeV average energy in inverse kinematics using a liquid hydrogen target. In the Doppler corrected γ ray spectrum, a single peak with an energy of 1089(15) keV appeared corresponding to the first excited state of 17B. Based on the reaction cross section, β2pp′ deformation parameter of the transition is deduced by distorted wave analysis. Comparing it with the electric quadrupole moment of the nucleus, it is shown that the deformation of the neutron distribution is large (βn∼0.6), and the neutron effective charge is much smaller (en<0.12) than usual (∼0.5). The small effective charge is interpreted as a consequence of the decoupling of valence neutrons from the core.

In-beam γ-ray spectroscopy of neutron-rich boron isotopesB15,17via inelastic scattering onC12

Low-lying bound states of the neutron-rich boron isotopes, $^{15}\mathrm{B}$ and $^{17}\mathrm{B}$, have been investigated using the $^{15,17}\mathrm{B}+^{12}\mathrm{C}$ inelastic scatterings at approximately 70 MeV/nucleon. In-beam \ensuremath{\gamma}-ray spectroscopy was used to determine the energy levels of the excited states, and the angular distribution of the particle in the inelastic channel populating each state was measured. Two bound states were observed for $^{15}\mathrm{B}$, while a new bound excited state was found for $^{17}\mathrm{B}$ at ${E}_{x}=1.07(1) \mathrm{MeV}$ very close to the neutron emission threshold $({S}_{2n}=1.39 \mathrm{MeV})$. The angular distributions for the transitions to these states are well reproduced with $\ensuremath{\Delta}{L}^{\ensuremath{\pi}}={2}^{+}$ diffraction patterns. The energy levels and $\ensuremath{\Delta}{L}^{\ensuremath{\pi}}={2}^{+}$ are consistent with shell model predictions. The quadrupole deformation lengths for the transitions extracted from the differential cross sections are compared to the shell model, suggesting a strong quenching of the neutron effective charge both for $^{15}\mathrm{B}$ and $^{17}\mathrm{B}$.

High-spin isomers and three-neutron valence configurations in 211Pb

Deep-inelastic reactions between a beam of 1360 MeV 208Pb ions and a thick 238U target have been used to populate the neutron-rich nucleus 211Pb. The observation of its γ decay has allowed identification of excited states up to the highest spin which can be formed from the three valence neutrons, including identification of three high-spin isomers. Level energies and transition strengths are compared to shell-model calculations with empirical interactions and predictions are made for the expected behaviour of more neutron-rich lead isotopes. The evidence for a possible increase in the neutron effective charge moving away from the N=126 shell gap is evaluated.

Shell model calculations with modified empirical Hamiltonian in the 132Sn region

Using recent experimental information for the 132Sn region, an empirical Hamiltonian is obtained by some modifications of a Hamiltonian (CW5082) originally derived from the 208Pb region. Shell model calculations with the new Hamiltonian show a remarkable improvement in the predictive power when compared with the available experimental results. It overcomes many limitations of the CW5082 Hamiltonian in this region, specially for $N\geq 84$ isotones. The calculated level spectra and B(E2) values with the new Hamiltonian, also compare well with the available results calculated with the CD-Bonn and SKX Hamiltonians, reflecting consistency in the wave function structure at least in the low-lying regions. An interesting behaviour of effective charges is revealed in this region. It is shown that a drastic reduction of proton effective charge is necessary for obtaining B(E2) values for the N = 84 isotones. Neutron effective charge is found to be in the range (0.62-0.72)e. We predict the spectroscopic properties of 135,136Sn not yet known experimentally. Further improvement of the modified Hamiltonian is also initiated.

Nuclear electromagnetic moments. [formula omitted]-NMR and its applications

Studies of magnetic moments and electric quadrupole moments for light unstable nuclei, which have been opened up by the recent development of spin-polarized radioactive nuclear beams and the β-ray detected nuclear magnetic resonance technique, are reviewed. The results lead to several intriguing findings concerning structures and interactions in unstable nuclei far from the stability line, such as a proton-halo structure in proton-rich nuclei, displacement of the single particle levels and quenching of the neutron effective charge in neutron-rich nuclei, and an anomalously large spin expectation value in a T=3/2 mirror pair. Applications of the present techniques to the study of hyperfine interactions of radioactive atoms introduced in solids are also discussed.

Measurements of the Electric Quadrupole Moment of Nb and Zr Isotopes with Modulated Adiabatic Fast Passage after Recoil Implantation into hcp Co

We report a new method for the measurement of quadrupole moments of radioactive nuclei which were not accessible with other techniques until now: modulated adiabatic fast passage on oriented nuclei (MAPON) after recoil implantation into hcp Co. Quadrupole moments of Zr and Nb isotopes were determined which are interesting in the context of the proton and the neutron effective charge at $A\ensuremath{\sim}90$.

Retardation of single-particle E1 transitions from the 622 keV broad d-wave neutron resonance in 9Be

Capture gamma rays from the 622 keV d-wave neutron resonance in 9Be with large reduced neutron width have been observed by means of a time-of-flight method, employing an anti-Compton NaI(TI) detector. Partial radiative widths have been derived for the strong primary E1 transition to the 3368 keV (2 +) state in 10Be and also for the weak one to the 5958 keV (2 +) state. Those widths were compared with predictions of the Lane-Mughabghab valence-capture model. As a consequence we found certain evidence to show that the 3368 keV state transition is appreciably hindered. The discrepancy can be removed by using a renormalized neutron effective charge which takes into account the coupling between the d-state neutron single-particle motion and the E1 giant resonance excitation of the target nucleus.

Electric and magnetic dipole transitions from broad s-wave neutron resonance in even-even sd-shell nuclei.

Observations have been performed for electromagnetic transitions from the broad {ital s}-wave neutron resonances at 658 keV in {sup 24}Mg, at 180 keV in {sup 28}Si, and at 103 keV in {sup 32}S. Capture gamma rays were measured with an anti-Compton NaI(Tl) detector, using a neutron time-of-flight technique. {ital E}1 and {ital M}1 transitions from those resonances to low-lying states with a strong single-particle character were found. The deduced partial radiative widths for {ital E}1 transition are in excellent agreement with the Lane-Mughabghab valence-capture model calculations taking the neutron effective charge, {minus}{ital Ze}/{ital A}. Moreover, it is shown that essential features of the observed {ital E}1 and {ital M}1 transitions can be well explained by assuming a configuration-mixing wave function, {Psi}{sub {ital i}}(1/2{sup +})={ital a}(0{sup +}{direct product}1/2{sup +})+{ital b}(1{sup +}{direct product}1/2{sup +})+{ital c}(1{sup +}{direct product}3/2{sup +}), for each resonance. The {ital M}1 transition strengths are compared also with more detailed shell model calculations in the model space of full ({ital sd}){sup {ital n}} configurations, using the Wildenthal effective interaction.

Mass dependence of effective charges in the interacting-boson model.

The mass dependence of the E2-boson effective charges in the interacting-boson model is tested by comparison with measurements of B(E${2;0}_{1}^{+}$\ensuremath{\rightarrow}${2}_{1}^{+}$) for $^{142}$,144,146,148,15 $^{0}\mathrm{Nd}$. This mass dependence originates from g-boson renormalization effects. The magnitude of this renormalization, as required to reproduce experiment, is consistent with an earlier estimate based on the renormalizations of the single boson energies. The proton effective charge is found to be larger than the neutron effective charge, in agreement with the shell model, but in contrast to an earlier report.

Shell structure of collective states inFe56,Fe58, andFe60

Conventional shell-model calculations of the iron isotopes with $A=56\ensuremath{-}60$ are discussed. The calculated level spectra are in good agreement with experiment. The calculations of $E2$ observables are in reasonable agreement with experiment when added effective charges of $1.0e$ are used for both neutrons and protons. The neutron effective charge is significantly different from one appropriate ($1.9e$) for $^{56}\mathrm{Ni}$. There is a strong state dependence in the effective $M1$ operator, and calculations of $M1$ observables are in general disagreement with experiment. An analysis of the structure of ground-state bands and yrast levels is made in terms of a simple rotational model. In all even isotopes, the intrinsic quadrupole moments in the ground-state "band" shrink dramatically with increasing $J$. There is evidence of a band crossing in all three even isotopes, but no evidence is found for an abrupt shape change in the ground-state bands of these nuclei. It is concluded that no simple rotational model gives a good description of the low-lying states of the iron isotopes.NUCLEAR STRUCTURE $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{59}\mathrm{Fe}$, $^{60}\mathrm{Fe}$, calculated levels. $^{56}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{60}\mathrm{Fe}$, calculated $B(M1)$, $B(E2)$, $\ensuremath{\mu}$, branching ratios. Shell model, Vervier interaction, Horie-Ogawa interaction, effective operators. Comparison with experiment and rotational model.

Interplay of valence-shell clusters and the vibrational field in58Ni

The level scheme and electromagnetic properties of58Ni are described in the two-particle cluster core coupling model without parameter fitting. The present results are compared to previous shell-model and quasi-particle calculations. To explain the enhancedE2 transitions a neutron effective charge ofe is needed, while the bare value for the vibrator charge has been used.

Retardation of E1 transitions and the neutron effective charge in 29Si

The effect of the giant dipole resonance on E1 transition rates is investigated, and an expression is derived which allows E1 effective charges to be calculated using the γ-absorption cross section of the neighbouring even-mass core. It is shown how this expression can be approximated using a sum rule in cases where the absorption cross section is not adequately known. Application is made to 29Si; using wave functions from a particle-core model, calculated E1 transition rates are in excellent agreement with experiment.

Electromagnetic Transition Rates inNi58

Lifetimes of 15 excited states in $^{58}\mathrm{Ni}$ and one in $^{62}\mathrm{Ni}$ have been measured using the Doppler-shift-attenuation method. The levels were excited via inelastic proton scattering at bombarding energies from 7 to 9 MeV. The Doppler shifts of decay $\ensuremath{\gamma}$ rays were measured in a 30-${\mathrm{cm}}^{3}$ Ge(Li) detector in coincidence with particles backscattered near 170\ifmmode^\circ\else\textdegree\fi{}. Theoretical estimates of stopping powers were checked experimentally by Dopplershift-attenuation measurements; excellent agreement was found. The matrix elements extracted from the measured lifetimes are compared with shell-model and vibrational-model predictions. Agreement is, in general, poor. The theoretical analysis indicates that a state-dependent neutron effective charge must be taken into account, and that core excitations play an important role in the determination of transition probabilities.

Microscopic Theory of Effective Operators for Electromagnetic Interactions in Nuclei

Effective operators for valence (open-shell) nucleons only are constructed, for electromagnetic interactions in nuclei. Such operators are calculated in terms of excitations and deexcitations of particle-hole pairs of the oore nucleons. The nuclear force involved is a realistic; nucleon-nucleon potential (Yale-Shakin). The theory is applied to the Sn region described in terms of five valence neutron subshells and of all the core and open subshells of both the neutrons and protons between the magic numbers 8 and 126. The effective quadrupole charge matrix has all the elements of about the same order of magnitude,thus giving a first partial support to the concept of a oonstant neutron effective charge. Calculations of observables are performed with the states of the even tin isotopes described in terms of the twoand fourquasiparticle Tamm-Dancoff theories involving explicitly only the valence neutrons. Results are presented for the B(E2, 2, * 0 . ) t the quadrupole moment Q ( 2 ) , the gyromagnetic factor g and the inelastic electron-scattering form factors for the 2+ and 3r 116 — XI states of Sn . Except for the last (3-* ) form factor, a good seraiquantitative agreement with all the corresponding experimental data is obtained. The reported calculations involve no ad hoc adjustable parameter.

Shell-Model Theory ofPb206

A detailed nuclear shell model calculation of the energy levels and gamma-ray transition rates in ${\mathrm{Pb}}^{206}$ is carried through. For pure singlet two-body forces with the same effective range and strength as for the low-energy two-body system, energy level agreement is good---for 13 known levels, the mean discrepancy between theory and experiment is 0.057 Mev. For singlet forces 75% as strong as for the low-energy two-body system, plus weak coupling to collective vibration, the energy level agreement is somewhat better---the mean discrepancy between theory and experiment is 0.035 Mev per level. In the latter theory, the strength of collective motion is determined from the known Coulomb excitation cross section in ${\mathrm{Pb}}^{206}$. In either theory, the calculated transition rates are in qualitative accord with experiment, but quantitative agreement is lacking.Electric quadrupole transition rates are shown to be describable in terms of a neutron effective charge. The effective charge is about $1.15e$ and the same in ${\mathrm{Pb}}^{206}$ as in ${\mathrm{Pb}}^{207}$. Other calculated quantities in good agreement with experiment are the relative cross sections to final $p$ states in the ${\mathrm{Pb}}^{206}(d, p){\mathrm{Pb}}^{207}$ reaction and the difference in binding energies of the last neutron in ${\mathrm{Pb}}^{206}$ and ${\mathrm{Pb}}^{207}$. The results are shown to be insensitive to substantial amounts of triplet-odd force, either attractive or repulsive.