Monopole Shifts Research Articles

Neutron-hole strength in N=81 nuclei

A systematic study of neutron-hole strength in the N = 81 nuclei 137Ba, 139Ce, 141Nd and 143Sm is reported. The single-neutron removal reactions (p,d) and (3He,4He) were measured at energies of 23 and 34 MeV, respectively. Spectroscopic factors were extracted from measured cross sections through a distorted-wave Born approximation analysis and centroids of single-particle strength have been established. The change in these centroid energies as a function of proton number have been compared to calculations of the monopole shift for the s1/2 and h11/2 orbitals, where the majority of the strength has been observed. Significant fragmentation of strength was observed for the d and g7/2 orbitals, particularly for the latter orbital which is deeply bound, with summed strengths that indicate a significant amount lies outside of the measured excitation energy range.

Proton Shell Evolution below Sn132 : First Measurement of Low-Lying β -Emitting Isomers in Ag123,125

The β-delayed γ-ray spectroscopy of neutron-rich ^{123,125}Ag isotopes is investigated at the Radioactive Isotope Beam Factory of RIKEN, and the long-predicted 1/2^{-} β-emitting isomers in ^{123,125}Ag are identified for the first time. With the new experimental results, the systematic trend of energy spacing between the lowest 9/2^{+} and 1/2^{-} levels is extended in Ag isotopes up to N=78, providing a clear signal for the reduction of the Z=40 subshell gap in Ag towards N=82. Shell-model calculations with the state-of-the-art V_{MU} plus M3Y spin-orbit interaction give a satisfactory description of the low-lying states in ^{123,125}Ag. The tensor force is found to play a crucial role in the evolution of the size of the Z=40 subshell gap. The observed inversion of the single-particle levels around ^{123}Ag can be well interpreted in terms of the monopole shift of the π1g_{9/2} orbitals mainly caused by the increasing occupation of ν1h_{11/2} orbitals.

Isomers and shell evolution in neutron-rich nuclei below the doubly magic nucleus 132Sn

The level structures of the very neutron-rich nuclei 128Pd82 and 126Pd80 have been investigated for the first time. A new isomer with a half-life of 5.8(8) μs in 128Pd is proposed to have a spin and parity of 8+ and is associated with a maximally aligned configuration arising from the g9/2Pd proton subshell with seniority υ = 2. The level sequence below the 8+ isomer is similar to that in the N = 82 isotone 130Cd, but the electric quadrupole transition that depopulates the 8+ isomer is more hindered in 128Pd than in 130Cd, as expected in the seniority scheme for a semi-magic, spherical nucleus. For 126Pd, three new isomers with Jπ = (5-), (7-), and (10+) have been identified with half-lives of 0.33(4) μs, 0.44(3) μs, and 23.0(8) ms, respectively. The smaller energy difference between the 10+ and 7- isomers in 126Pd than in the heavier N = 80 isotones can be interpreted as being ascribed to the monopole shift of the h11/2 neutron orbit. The nature of the N = 82 shell closure scrutinized with these characteristic isomers is discussed.

Relationship of scattering phase shifts to special radiation force conditions for spheres in axisymmetric wave-fields.

When investigating the radiation forces on spheres in complicated wave-fields, the interpretation of analytical results can be simplified by retaining the s-function notation and associated phase shifts imported into acoustics from quantum scattering theory. For situations in which dissipation is negligible, as taken to be the case in the present investigation, there is an additional simplification in that partial-wave phase shifts become real numbers that vanish when the partial-wave index becomes large and when the wave-number-sphere-radius product vanishes. By restricting attention to monopole and dipole phase shifts, transitions in the axial radiation force for axisymmetric wave-fields are found to be related to wave-field parameters for traveling and standing Bessel wave-fields by considering the ratio of the phase shifts. For traveling waves, the special force conditions concern negative forces while for standing waves, the special force conditions concern vanishing radiation forces. An intermediate step involves considering the functional dependence on phase shifts. An appendix gives an approximation for zero-force plane standing wave conditions. Connections with early investigations of acoustic levitation are mentioned and some complications associated with viscosity are briefly noted.

Monopole-driven shell evolution below the doubly magic nucleus 132Sn explored with the long-lived isomer in 126Pd.

A new isomer with a half-life of 23.0(8) ms has been identified at 2406 keV in (126)Pd and is proposed to have a spin and parity of 10(+) with a maximally aligned configuration comprising two neutron holes in the 1h(11/2) orbit. In addition to an internal-decay branch through a hindered electric octupole transition, β decay from the long-lived isomer was observed to populate excited states at high spins in (126)Ag. The smaller energy difference between the 10(+) and 7(-) isomers in (126)Pd than in the heavier N=80 isotones can be interpreted as being ascribed to the monopole shift of the 1h(11/2) neutron orbit. The effects of the monopole interaction on the evolution of single-neutron energies below (132)Sn are discussed in terms of the central and tensor forces.

Classical toy models for the monopole shift and the quadrupole shift

The penetration of s- and p(1/2)-electrons into the atomic nucleus leads to a variety of observable effects. The presence of s-electrons inside the nucleus gives rise to the isotope shift in atomic spectroscopy, and to the isomer shift in Mössbauer spectroscopy. Both well-known phenomena are manifestations of the more general monopole shift. In a recent paper (Koch et al., Phys. Rev. A, 2010, 81, 032507), we discussed the existence of the formally analogous quadrupole shift: a tensor correction to the electric quadrupole interaction due to the penetration of relativistic p(1/2)-electrons into the nucleus. The quadrupole shift is predicted to be observable by high-accuracy molecular spectroscopy on a set of 4 molecules (the quadrupole anomaly). The simple physics behind all these related phenomena is easily obscured by an elaborate mathematical formalism that is required for their derivation: a multipole expansion in combination with perturbation theory, invoking quantum physics and ideally relativity. In the present paper, we take a totally different approach. We consider three classical 'toy models' that can be solved by elementary calculus, and that nevertheless contain all essential physics of the monopole and quadrupole shifts. We hope that this intuitive (yet exact) analysis will increase the understanding about multipole shift phenomena in a broader community.

MONOPOLE SHIFT IN ODD NEUTRON-RICH F ISOTOPES: A SHELL MODEL DESCRIPTION

Monopole shift in the proton states in odd neutron-rich F isotopes has been studied with neutron number changing from N = 10 to 20 for three different interactions. The variation of monopole shift point out towards appearance of shell closure at N = 14 and N = 16 and its disappearance at N = 20. Low lying states of odd F isotopes have also been calculated in the limited configuration space of sd shells for these interactions.

Particle-hole intruder levels in 67Cu, collectivity, monopole shifts, and the hockey-stick behaviour of ℓ − 1/2 5/2− levels in neutron-rich odd-mass Cu nuclei

A new sequence of gamma rays with energies of 572, 499, 585, and 674 keV has been identified in 67Cu populating the 7/2− level at 2362 keV. Owing to the strong population of the 2362-keV level via an ℓ = 3 proton pickup reaction, that level is assigned to be an f7/2−1 2-particle-1-hole "intruder" proton configuration, and the new levels are found to form a sequence consistent with intruder sequences in the adjacent odd-mass Cu isotopes and in the odd-mass Sb isotopes. The changing position of the intruder sequence in the odd-mass Cu isotopes is discussed and related to the onset of collectivity associated with the presence of g9/2 neutrons beyond N = 40. The increase in collectivity is also discussed for a number of isotonic and isotopic chains as more protons or neutrons, respectively, are added beyond an oscillator shell boundary. For most of these systems, the ℓ −1/2 levels show a systematic "hockey-stick-like" behaviour with a sharp decrease in energy with the addition of the first protons or neutrons, owing to both the added collectivity and the tensor interaction, and then a lower slope when collectivity changes are diminished and only the tensor interaction is influencing the changes in level positions.

Discovery of 157W and 161Os

The nuclides 157W and 161Os have been discovered in reactions of 58Ni ion beams with a 106Cd target. The 161Os α-decay energy and half-life were 6890±12 keV and 640±60 μs. The daughter 157W nuclei β-decayed with a half-life of 275±40 ms, populating both low-lying α-decaying states in 157Ta, which is consistent with a 7/2− ground state in 157W. Fine structure observed in the α decay of 161Os places the lowest excited state in 157W with Iπ=9/2− at 318±30 keV. The branching ratio of 5.5−2.2+3.1% indicates that 161Os also has a 7/2− ground state. Shell-model calculations analysing the effects of monopole shifts and a tensor force on the relative energies of 2f7/2 and 1h9/2 neutron states in N=83 isotones are presented.

Beta-delayed γ-ray studies of πf7/2 - νpf shell nuclei

We have utilized the selective process of β decay to populate low-energy excited states in the neutron-rich 22Ti, 23V, 24Cr, and 25Mn nuclei. The goal was to systematically track the monopole shift of the νf5/2 single-particle level with increased occupancy of the πf7/2 orbital. The β-decay properties of the parent nuclides, along with the low-energy structure of the daughters, are presented and compared with the results of shell model calculations employing the GXPF1 interaction.

New level information on Z = 51 isotopes, 111Sb60 and 134, 135Sb83, 84

New data for low-spin low-energy levels in 111,134,135Sb are presented. The observed structures are compared to shell-model calculations. The monopole shifts for the d5/2 and g7/2 single-proton levels and the spin-orbit splitting for the d5/2 and d3/2 orbitals as N/Z moves from ∼1 up to 1.6 are discussed.

Shell-model description of monopole shift in neutron-rich Cu

Variations in the nuclear mean-field, in neutron-rich nuclei, are investigated within the framework of the nuclear shell model. The change is identified to originate mainly from the monopole part of the effective two-body proton-neutron interaction. Applications for the low-lying states in odd-$A$ Cu nuclei are presented. We compare the results using both schematic and realistic forces. We also compare the monopole shifts with the results obtained from large-scale shell-model calculations, using the same realistic interaction, in order to study two-body correlations beyond the proton mean-field variations.

Monopole shifts and extrapolations for the structure of nuclides near 122Zr

Monopole shifts and extrapolations for the structure of nuclides near 122Zr

Particle-core coupling around [formula omitted]Ni: a study of the subshell closure at N=40

The existence of a subshell gap at neutron number N=40 is investigated in the odd-mass Ni and Cu isotopes using the Particle-Core Coupling Model (PCM). The calculated properties are in good agreement with the existing experimental data, suggesting that 68Ni is a good core for the adjacent nuclei. Evaluation of the 2+1 excitation energies, two-neutron separation energies, and pairing properties of the Ni isotopes reveals discontinuities at neutron number N=40. These data support the existence of a significant neutron subshell gap at N=40, for Z=28. The systematic behavior of the proton single-particle energies extracted from the particle-core coupling calculations for the odd-mass Cu isotopes is discussed in terms of monopole shifts. The effect is consistent with the existence of a neutron subshell gap at N=40.

Strong interaction effects in pionic 208Pb

The X-ray spectrum of pionic 208Pb has been measured. The deduced values of the strong interaction monopole shift with respect to the point Coulomb energy are ϵ 0(4f) = 1.49±0.02 keV and ϵ 0(3d) = 19.4±1.2 keV. The observed s strong interaction absorption widths of this spherical nucleus are found to be Γ 0(4f) = 1.25±0.02 keV and Γ 0(3d) = 47.0±3.6 keV. Important in the analysis of the pionic 4f level is the intensity balance for this level, giving an additional check on the measured absorption width of the pionic 4f level. For the more peripheral 4f state the measured strong interaction shifts and widths are well explained by standard optical model calculations. The values for the 3d state, however, are not in agreement with these calculations.

Anomalous strong interaction in pionic Mg

The pionic 2p→1s transition has been observed in Mg. For the strong interaction monopole shift a value has been measured of ϵ 0(1s)=−81.6±0.6 keV with respect to the point Coulomb energy, in agreement with standard optical potential predictions. The observed strong interaction absorption width is Γ 0(1s)=17.2±1.6 keV, which is about a factor of 1.5 smaller than expected from presently available models. This measurement confirms the trend of “anomalously” small strong interaction widths for deeply bound pionic states already observed in heavier elements.

Determination of the effective quadrupole moment in 181Ta with pionic X-rays

From the hyperfine splitting of the 5g → 4f and the 6g → 4f pionic X-rays in 181Ta, an effective quadrupole moment of Q eff = 3.58±0.03 b was determined. The strong interaction monopole shift ε 0 and the width Γ 0 of the 4f level were measured to be ε 0 = 540±100 eV and Γ 0 = 225±57 eV. in good agreement with the values obtained with the standard optical potential description of the pion-nucleus interaction. Estimating the influence of the finite nuclear size, the deformation induced through the strong interaction between the pion and the finite nucleus, and the relative magnitude between the strong and the electromagnetic quadrupole coupling constants, we arrive at a value for the spectroscopic quadrupole moment of Q = 3.30±0.06 b, and for the intrinsic quadrupole moment of Q 0 = 7.06±0.12 b. This result is in good agreement with earlier values and with recent results reported from kaonic and muonic atoms as well as with the value obtained from Nilsson model calculations.

Monopole and quadrupole strong interaction effects in pionic atoms of 175Lu and 165Ho

We have measured the strong-interaction monopole energy shift ε 0 and width Γ 0, and the quadrupole splitting of the 4f level in pionic 175Lu and 165Ho. The monopole results are: ε 0(Lu) = 597 ± 70eV, ε 0(Ho) = 295 ± 80 eV, Γ 0(Lu) = 200 ± 70eV and Γ 0(Ho) = 190 ± 40eV. The monopole shift in the case of lutecium deviates from the value obtained with a standard optical potential description of the pion-nucleus interaction. Using the (electromagnetic) quadrupole moment as measured recently in an experiment on muonic 175Lu, we find for the strong-interaction quadrupole constant of the 4f state in 175Lu ε 2 = − 89 ± 29 eV. The ratio ε 2 ε 0 is in good agreement with theoretical predictions. We relax the usual assumption in the optical potential of a homogeneous mixture of neutrons and protons and show that ε 0 and ε 2 are mainly given by the generalized moment 〈 r κ e − αr 〉 ( κ = 3.93, α = 0.21 fm −1) of the monopole and the quadrupole density of the neutrons, respectively. We deduce from the measured monopole shifts the ratio R between the generalized monopole moment above and the value of the same moment if neutrons and protons are homogeneously mixed (the latter is taken from muonic atom data). The results are R(Lu) = 1.34 ± 0.16 and R(Ho) = 1.14 ± 0.26. The deviation of R(Lu) from unity may be interpreted in two ways: the optical potential in the present form is not sufficient for the analysis of the 4f level shift in π- 175Lu, or there is a difference between the neutron and proton monopole density distributions in this nucleus.