Odd-parity Levels Research Articles

Analysis of the Third Spectrum of Praseodymium*

The spectrum of doubly ionized praseodymium was recorded and analyzed, with the result that 118 energy levels of odd parity and 130 levels of even parity were derived. These include nearly all the levels of the 4f3, 4f25d, 4f26s, and 4f26p configurations as well as some low levels of the 4f5d2 and 4f26d configurations. Electrostatic and spin–orbit parameters were determined for the 4f26s configuration. From the hfs of the 4f26s levels, a magnetic dipole interaction constant of 0.46 cm−1 was obtained. An ionization potential of 23.2 V was calculated from levels of the 4f26d and 4f26d series.

Collective motion in the nuclear shell model III. The calculation of spectra

A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.

Nuclear Levels in a Number of Even-Even Rare Earths (150≤A≤184)

To obtain more data on the system of levels in even-even nuclei, a number of such nuclei ($150\ensuremath{\le}A\ensuremath{\le}184$) were studied with electron-capturing sources in permanent magnet spectrogaphs. Some measurements were made with scintillation counters. Data confirming recently reported results on the decay of ${\mathrm{Tb}}^{152}$, ${\mathrm{Tb}}^{156}$, and ${\mathrm{Ho}}^{162}$ have been obtained. It was found that ${\mathrm{Eu}}^{150}$ has two isomeric states (${T}_{\frac{1}{2}}=14$ hr and > 5 yr). Levels at 740.7 (0+) and 773.3 (4+) kev in ${\mathrm{Sm}}^{150}$ are proposed. A study of the two isomeric activities of ${\mathrm{Tb}}^{154}$ indicated the existence of levels in ${\mathrm{Gd}}^{154}$ which may be described as a gamma-vibrational band (at 997.3 kev) and a beta-vibrational band (at 680.6 kev). The new data for ${\mathrm{Tm}}^{166}$ (7.7 hr) are consistent with levels in ${\mathrm{Er}}^{166}$ at 2137.3 and 2164.6 kev, both of which are probably 3 states and which exhibit considerably different branching ratios of the de-exciting transitions. The decay of ${\mathrm{Lu}}^{172}$ appears to populate a large number of even-parity levels in ${\mathrm{Yb}}^{172}$ which may be arranged in rotational bands corresponding to primary or base states at 1174.0 kev ($I=3+$), 1467.5 kev ($I=2+$), 1664.3 kev ($I=3+$), 1702.1 kev ($I=3+$), 2075.0 kev ($I=4+$), and 2287.3 kev ($I=4+$). The very complex decay of the two isomers of ${\mathrm{Re}}^{182}$ excite many odd-parity levels which may be arranged in seven or more bands. In addition, even-parity beta- and gamma-vibrational bands may be populated. Electron-capture decay of ${\mathrm{Re}}^{184}$ populates a gamma-vibrational band in ${\mathrm{W}}^{184}$ of spins 2, 3, and 4. Data relevant to the rotational energy parameters and ratios of gamma-ray transition probabilities from the various states are presented. As a corollary, data on the decay of ${\mathrm{Eu}}^{149}$ are presented since this activity was present in some of our composite sources.

Protons and deutrons from Ni58 bombarded by 14.8 MeV neutrons

Using a counter telescope, energy spectra and angular distributions are measured for protons emitted from Ni58 at 14.8 MeV incident neutron energy. The angular distributions indicate for the direct interaction contribution l = 0 and l = 2 transitions to unresolved levels near the ground state of the residual Co58 nucleus. Transitions with l = 1 to states of higher excitation demonstrate the presence of odd parity levels. Below 6 MeV proton energy, the distributions are isotropic. Nuclear temperatures of 1.35±0.03 MeV and 0.50±0.03 MeV are found for the reactions (n, pγ) + (n, pn) and (n, np) respectively. The total cross section for proton emission is 830±70mb. Partial cross sections are: (n, pγ) + (n, pn) 430 mb compound nucleus, 60 mb direct interaction; (n, np) 340 mb.Deuteron emission is established, the total cross section for the (n, d) reaction being 25±6 mb. The angular distribution of the most prominent deuteron group suggests unresolved transitions to the 7/2− Co57 ground state and a new state at approximately 0.5 MeV. The presence of an l = 1 transition implies approximately 13% p-wave admixture in the Ni58 ground state configuration.

"Repulsion of Energy Levels" in Complex Atomic Spectra

It is shown that "repulsion of energy levels" of the same symmetry type occurs in complex atomic spectra. Thus, for the elements Hf, Ta, W, Re, Os, and Ir, for which the spin-dependent forces are relatively strong, the spacings between neighboring odd-parity levels of the same $J$ value follow the Wigner distribution (approximately). For the elements Sc, Ti, V, Cr, Mn, Fe, Co, and Ni, for which the spin-dependent forces are relatively weak, a similar distribution is obtained for the odd-parity levels having fixed values for $S$, $L$, and $J$. (When the quantum numbers $S$ and $L$ are disregarded, the same levels give rise to a distribution of spacings which is approximated by a random superposition of a number of appropriately weighted Wigner distributions.) For the elements Y, Zr, Nb, Mo, Ru, Rh, and Pd, for which the spin-dependent forces are of intermediate strength, the empirical distribution of spacings between the odd levels of the same $J$ value has a character which is intermediate between the Wigner and exponential distributions. All of these observations are explained in terms of a statistical model for the Hamiltonian matrix in the $S$, $L$, $J$, $\ensuremath{\pi}$ representation. Quantitative results are obtained for a relatively simple form of the model which depends on only two parameters, viz., the dimensionality $N$ and the ratio $\ensuremath{\mu}$ of the dispersions of the normal distributions for the off-diagonal and diagonal matrix elements. The transition from the exponential to the Wigner distribution occurs, roughly speaking, in the range of $N{\ensuremath{\mu}}^{2}$ from 0 to 1. The results of this work suggest that an empirical study of the distribution of the spacing between the energy levels of a complex quantum system may be capable of pointing to the existence of constants of the motion beyond those which are already known.

Studies of Decay Schemes in the Osmium-Iridium Region. II. Decay of 12-DayIr190

Spectra of the gamma rays and internal conversion electrons emitted in the decay of 12-day ${\mathrm{Ir}}^{190}$ have been studied in detail. Internal conversion spectra were obtained with the aid of double-focusing and intermediate-image beta spectrometers, and a permanent-magnet spectrograph. Gamma-ray spectra were obtained by means of photoelectric conversion, employing a double-focusing spectrometer, and by scintillation techniques.These measurements of the energies and relative intensities of gamma rays and internal conversion electrons give internal conversion coefficients for a number of transitions. These data, coupled with co-incidence studies of gamma rays, support the level scheme reported by Nielsen et al. for ${\mathrm{Os}}^{190}$ and establish new, odd-parity levels at 1384, 1568, and 1876 kev. An upper limit of 2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ is set on positron branching in the decay of ${\mathrm{Ir}}^{190}$. Relative electron capture transition probabilities for the decay of ${\mathrm{Ir}}^{190}$ to ${\mathrm{Os}}^{190}$ and ratios of reduced transition probabilities for electromagnetic transitions from a number of levels of ${\mathrm{Os}}^{190}$ follow from these results. They are compared with the predictions of the strong-coupling model and the asymmetric rotor model. The half-life of ${\mathrm{Ir}}^{190}$ was found to be 12.3\ifmmode\pm\else\textpm\fi{}0.4 days. Even-$A$ iridium-osmium total disintegration energies are found to rise substantially above the values predicted by semiempirical mass formulas, suggesting a possible effect of the change in the nuclear deformation in this region.

Shell Model Assignments for the Energy Levels ofC14andN14

Electromagnetic transition widths, reduced widths, and inelastic scattering cross sections are calculated for the following states of ${\mathrm{N}}^{14}$ and ${\mathrm{C}}^{14}$: (1) The levels arising from the ground-state configuration, ${s}^{4}{p}^{10}$, (2) the odd-parity levels arising from excitation of a $1p$ nucleon into the degenerate $2{s}_{\frac{1}{2}}$ and $1{d}_{\frac{5}{2}}$ shells, (3) the even-parity group of levels formed by excitation of two $1p$ nucleons into the $2s$ and $1d$ shells. The calculations for the ${s}^{4}{p}^{10}$ configuration are carried out using the wave functions of Elliott and of Visscher and Ferrell, and in $\mathrm{jj}$ coupling. The calculations for the odd-parity levels are done in the $\mathrm{jj}$-coupling scheme. For the even-parity excited configuration an inert ${\mathrm{C}}^{12}$ core is assumed and $M1$ radiative widths are calculated for states arising from ${s}^{2}+{d}^{2}+sd$. The calculations are compared to the existing data. On the basis of this comparison shell-model assignments are proposed for 19 of the 27 known levels below 11-Mev excitation in ${\mathrm{N}}^{14}$ and for all the known levels in ${\mathrm{C}}^{14}$ below 9-Mev excitation.

C13(p, γ)N141.47- and 2.11-Mev Resonances and the Odd-Parity Levels of Mass 14

A study has been made of the $\ensuremath{\gamma}$ rays emitted by the 8.9- and 9.5-Mev levels of ${\mathrm{N}}^{14}$ using the ${\mathrm{C}}^{13}(p, \ensuremath{\gamma}){\mathrm{N}}^{14}$ reaction at the 1.47- and 2.11-Mev resonances. The decay schemes of these levels were reinvestigated using a three-crystal pair spectrometer, NaI(Tl) single-crystal measurements, and standard $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence techniques. The anisotropies relative to the bombarding beam of most of the observed $\ensuremath{\gamma}$ transitions were measured using the three-crystal pair spectrometer. The angular distributions of some of the $\ensuremath{\gamma}$ transitions were measured using a single NaI(Tl) crystal. Measurements were made of the Doppler shifts of the ground state decay of the ${\mathrm{N}}^{14}$ 5.10-Mev level and the cascade from the ${\mathrm{N}}^{14}$ 5.83-Mev level to the ${\mathrm{N}}^{14}$ 5.10-Mev level. From these Doppler shift measurements the mean lifetime of the ${\mathrm{N}}^{14}$ 5.83-Mev level was found to be in the range (5.65)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ sec; while an upper limit of 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec was set on the mean life of the ${\mathrm{N}}^{14}$ 5.10-Mev level. The results of the study of the $\ensuremath{\gamma}$ decay of the ${\mathrm{N}}^{14}$ 9.5- and 8.9-Mev levels combined with the results of earlier measurements give conclusive assignments of ${2}^{\ensuremath{-}}$, ${3}^{\ensuremath{-}}$, 3, and 2 for the ${\mathrm{N}}^{14}$ levels at 9.50, 8.90, 5.83, and 5.10 Mev. The 5.83-Mev level most probably has odd parity. A tentative assignment of $J=2$ is given to the ${\mathrm{N}}^{14}$ 7.02-Mev level. Evidence is presented, from this and previous investigations, that indicates the ${\mathrm{N}}^{14}$ 8.06-, 8.70-, 8.90-, and 9.50-Mev levels arise from the ${s}^{4}{p}^{9}2s$ and ${s}^{4}{p}^{9}d$ configurations with the largest contribution being from the (${p}_{\frac{1}{2}}2{s}_{\frac{1}{2}}$) configuration for the 8.06- and 8.70-Mev levels and from the (${p}_{\frac{1}{2}}{d}_{\frac{5}{2}}$) configuration for the 8.90- and 9.50-Mev levels. The analogs of these $T=1$ levels in ${\mathrm{C}}^{14}$ are almost certainly the ${\mathrm{C}}^{14}$ 6.09-, 6.89-, 6.72-, and 7.35-Mev levels, respectively. The $T=0$, ${s}^{4}{p}^{9}2s$ and ${s}^{4}{p}^{9}d$ states of ${\mathrm{N}}^{14}$ are also discussed. It is proposed that the 4.91-, 5.69-, 5.10-, and 5.83-Mev levels of ${\mathrm{N}}^{14}$ are ${0}^{\ensuremath{-}}$ and ${1}^{\ensuremath{-}}$, ${s}^{4}{p}^{9}2{s}_{\frac{1}{2}}$ and ${2}^{\ensuremath{-}}$ and ${3}^{\ensuremath{-}}$, ${s}^{4}{p}^{9}{d}_{\frac{5}{2}}$ states, respectively.

The odd-parity states of 16 O and 16 N

The properties of the odd-parity states of 16 O and 16 N have been calculated insofar as they may be considered to arise from the configurations p -1 d and p -1 2s . The calculations were performed in intermediate coupling, including the spin-orbit splittings of the p and d shells, and full account was taken of the mixing of the two configurations. A satisfactory picture can be given of the known odd-parity levels of both nuclei, although some anomalous features, apparently associated with the detailed nature of nuclear forces, remain without full explanation. Some remarks are made regarding the photodisintegration of oxygen and it is found that the shell model can account satisfactorily for the observed photon widths which constitute the giant resonance.

Independent-Particle Model of the Nucleus. III. The Calcium Isotopes

The isotopes of calcium of mass number 41, 42, and 43 are analyzed using the methods given in papers I and II of this series. It is found that the experimental data on ${\mathrm{Ca}}^{41}$ and ${\mathrm{Ca}}^{42}$ is sufficient to predict the low-lying odd-parity levels of ${\mathrm{Ca}}^{43}$ as well as the magnetic moment. Detailed agreement between theory and experiment is obtained for the levels of ${\mathrm{Ca}}^{43}$ of spin and parity $\frac{7}{{2}^{\ensuremath{-}}}$, $\frac{5}{{2}^{\ensuremath{-}}}$, $\frac{3}{{2}^{\ensuremath{-}}}$, and $\frac{9}{{2}^{\ensuremath{-}}}$ and the experimental Schmidt line magnetic moment deviation of 0.595 nm is in agreement with a predicted deviation of 0.60 nm. The relative importance of particle forces and surface forces due to collective motion is investigated and it is concluded that for the isotopes investigated the surface forces are so weak as to have a negligible effect on the level spacings. As a measure of the upper limit of the strength of the surface forces the magnitude of $\ensuremath{\hbar}\ensuremath{\omega}$ (the surfon energy) is set at \ensuremath{\gtrsim}15 Mev. An effective two-particle interaction potential is derived which differs to some extent from the two-particle scattering potential in that it has a longer range and is more shallow.

The Excited States of theN13Nucleus

The properties of the excited states of ${\mathrm{N}}^{13}$ were reinvestigated by applying dispersion theory to the ${\mathrm{C}}^{12}(p, p){\mathrm{C}}^{12}$ differential cross section reported in the preceding paper. The quantity and accuracy of the data were sufficient to permit extraction of the experimental $S$ wave phase shift up to 1.4 Mev. The remainder of the data was fitted by successive readjustment of the level parameters.The present analysis corroborates the previous momentum and parity assignments but gives somewhat different values for the resonant energies and widths. The level assignments together with the revised widths and resonant energies are as follows: The 0.46-Mev scattering anomaly is due to a virtual ($j=\frac{1}{2}, +$) level in the compound nucleus ${\mathrm{N}}^{13}$ with ${E}_{r}=2.369$ Mev and $\ensuremath{\Gamma}=31$ kev. The 1.7-Mev scattering anomaly is the result of two virtual levels, a ($j=\frac{3}{2}, \ensuremath{-}$) level with ${E}_{r}=3.511$ Mev and $\ensuremath{\Gamma}=55$ kev and a ($j=\frac{5}{2}, +$) level with ${E}_{r}=3.558$ Mev and $\ensuremath{\Gamma}=61$ kev. ${E}_{r}$ and $\ensuremath{\Gamma}$ are calculated in the center-of-mass system and ${E}_{r}$ is measured from the ground state of ${\mathrm{N}}^{13}$. These new values for ${E}_{r}$ and $\ensuremath{\Gamma}$ agree quite well with those obtained from the ${\mathrm{C}}^{12}(p, \ensuremath{\gamma}){\mathrm{N}}^{13}$ reaction provided it is assumed that the ($j=\frac{5}{2}, +$) level does not participate appreciably in the capture process. The values of the reduced widths of the levels indicate that the two even-parity levels arise mainly from single particle excitation, but that the odd-parity level involves appreciable excitation of the core.