Quadrupole Transition Probabilities Research Articles

Even nuclei without an axis of symmetry

The low lying levels of even nuclei, and the electric quadrupole transition probabilities between certain of these levels, are discussed in terms of the rotation of a nucleus without axial symmetry. The moments of inertia of the nucleus are not restricted to those prescribed by the hydrodynamical model. Rather we use a prescription due to Moszkowski. This contains a parameter p whose value depends on the residual interaction, and which in varying from 0 to 1 causes the moments of inertia to vary from the rigid body values to approximately the hydrodynamical values. We find that to obtain agreement with the experimental data on the transitions it is necessary to have p larger than the values which give the correct values of the energy of the first excited state in the case of nuclei having a small deviation from axial symmetry.

Inelastic Scattering of 4-Mev Protons and Deuterons from Separated Isotopes ofDy161,Dy163,Yb171, andYb173

The inelastic scattering of protons and deuterons from the odd isotopes of Dy and Yb has been measured at energies around 4 Mev in a heavy-particle spectrometer at a scattering angle of 145\ifmmode^\circ\else\textdegree\fi{}. Isotopically pure targets were prepared in an electromagnetic isotope separator. Inelastic groups corresponding to the two lowest rotational states were observed in ${\mathrm{Dy}}^{161}$ at 44 kev and 102 kev, in ${\mathrm{Dy}}^{163}$ at 74 kev and 170 kev, in ${\mathrm{Yb}}^{171}$ at 67 kev and 76 kev, and in ${\mathrm{Yb}}^{173}$ at 78 kev and 181 kev. The reduced electric quadrupole transition probabilities for these levels were determined.

Electric Excitation of Certain Rare-Earth Nuclei by Protons

Sixteen energy levels have been observed in thirteen isotopes of samarium, europium, gadolinium, and terbium. Electric quadrupole transition probabilities have been determined for some of these energy levels from the measured electric excitation cross sections. For the even-$A$ isotopes of Gd, the properties of the low-lying energy levels are in good agreement with the expectations of the strong coupling rotational model. The first energy levels in the even isotopes of samarium show the sharp break in the position of the first excited level which has recently been pointed out by Scharff-Goldhaber. In general, the results are in good qualitative agreement with the predictions of the collective model; however, the moments of inertia for the rotational levels observed in this region are substantially larger than those expected from the intrinsic deformations obtained from the radiative transition probabilities.

Dipole and Quadrupole Transition Probabilities in Neutron-Capture Gamma Radiation

An analysis of the intensities of neutron-capture $\ensuremath{\gamma}$ rays in even-charge nuclei shows that at high energies the emission probability of $E1$ radiation is greater than that of any other multipole order. This conclusion is supported by additional evidence from odd-charge nuclei. In three nuclei (${\mathrm{Mg}}^{25}$, ${\mathrm{Si}}^{29}$, and ${\mathrm{S}}^{33}$) a direct comparison shows that (at the same energy) the emission probability of $E1$ is 200 times greater than that of $M1$ radiation. The rate of emission of $E2$ radiation has been compared directly with $E1$ radiation in only one instance, viz., ${\mathrm{Mg}}^{25}$, where (at 7 Mev) it was found to be lower by a factor of 2000. Further evidence is adduced to show that this ratio is not exceptional and that the rate of emission of $E2$ radiation (at 7 Mev) is less than that of $M1$ radiation. The absolute rates of emission for $E1$ and $M1$ $\ensuremath{\gamma}$ rays are evaluated in those instances where the radiation width of the capturing state is known. When corrected for the level spacing near the initial state (and for the nuclear radius, in the case of $E1$ radiation), the rates of emission are remarkably constant; they are independent of the nuclear charge and mass over a range where the level spacing may vary by a factor of ${10}^{4}$ or more. The emission rates of $E1$ and $M1$ radiation are generally ten times lower than those predicted by the formula of Weisskopf, which is based on the independent-particle model. The emission rates do not exceed those expected from that formula in the case of the exceptionally strong $M1$ ground-state $\ensuremath{\gamma}$ rays from ${\mathrm{F}}^{20}$ and ${\mathrm{Al}}^{28}$. It is shown that the identification of the spins and parities of excited states in many nuclei can be made on the basis of intensity measurements. Finally, the influence of closed shells on the $\ensuremath{\gamma}$-ray spectra is discussed.

Interaction Effects on Radiative Transitions in Nuclei

Electromagnetic transition processes in nuclei are considered on the assumption that the influence of an external electromagnetic field on a nucleus can be incorporated into a guage invariant Schroedinger equation for the nucleons (phenomenological theory). From the results of the preceding paper it is concluded that equations for electric multipole transition probabilities have the usual form but that the $f$-sum rule is modified in a manner depending on the nuclear interactions. Explicit expressions for the generalization of the $f$-sum rule to all electric multipole orders are given for exchange and velocity dependent interactions. The magnetic multipole moments,and therefore the corresponding transition probabilities, depend markedly on the form of the interaction with the electromagnetic field. General formulas are given for all magnetic multipole moments of nuclei in which exchange forces and velocity dependent interactions play a role. In addition it is possible to incorporate into the theory the spin-antisymmetric addition to the magnetic dipole moment implied by the static moments of ${\mathrm{H}}^{3}$ and ${\mathrm{He}}^{3}$.Detailed application is limited in this paper to magnetic dipole transitions. The theoretical cross section for the capture of thermal neutrons by protons is found to have about a 4 percent addition, due entirely to the spin-antisymmetric term. In heavier nuclei this spin term, exchange interactions, and the velocity interaction proposed to account for high energy nucleon-nucleon scattering contribute to the magnetic dipole transitions. The ratio of magnetic dipole to electric quadrupole transition probabilities is of the order of ${(\frac{25}{\ensuremath{\hbar}\ensuremath{\omega}})}^{2}{A}^{\ensuremath{-}\frac{4}{3}}$, where $A$ is the nuclear mass number and $\ensuremath{\hbar}\ensuremath{\omega}$ is the photon energy in Mev. Similar emphasis of the magnetic over electric transitions at low energies is anticipated for higher multipole orders, so interpretations of isomeric transitions on the basis of lifetime require re-examination.

Possibility of Measuring a Quadrupole Transition Probability from an Auroral Afterglow

THE green auroral line of oxygen at 5,577 A. (1D2 – 1D0) has been found by Vegard and Kvifte1, and Jenkins, Bowtell and Strong2 in the afterglow of a Tesla discharge through argon, or a mixture of argon and nitrogen, at nearly atmospheric pressure, when there is a minute trace of oxygen present. It is accompanied by a diffuse band similar to one described by L. and R. Herman3. We have made some measurements of the decay of this phosphorescence, which can be followed by a photo-multiplier connected through an amplifier to a cathode ray oscillograph with a low-frequency time base. Three sources have been used, namely, two 300-watt commercial Osram gas-filled lamps, and a cylindrical tube 21 cm. long and 6 cm. in diameter containing a similar gas mixture, with two rod electrodes 2 mm. in diameter, mounted near one end with their tips 3 cm. apart. The photomultiplier was exposed to the glow from a volume of gas about 3 cm. in linear dimensions.

The Computation of Quadrupole and Magnetic-Dipole Transition Probabilities

The theory of quadrupole radiation is formulated in such a fashion as to make available all the methods of computation and sum rules which have been developed for electric-dipole radiation. Formulas for the strengths are given for the $\mathrm{SL}{M}_{S}{M}_{L}$ scheme as well as the $\mathrm{SLJM}$ scheme. The problem of the relative strengths of the multiplets in a transition array is treated, and formulae are given that explicitly solve this problem for all possible transitions between two-electron configurations. Values for $\mathrm{np}{n}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\leftrightharpoons}\mathrm{np}{n}^{\ensuremath{'}\ensuremath{'}}p$, $\mathrm{np}{n}^{\ensuremath{'}}p\ensuremath{\leftrightharpoons}n{p}^{2}$, $\mathrm{np}{n}^{\ensuremath{'}}p\ensuremath{\rightarrow}\mathrm{np}{n}^{\ensuremath{'}}P$ and $n{p}^{2}\ensuremath{\rightarrow}n{p}^{2}$ are tabulated. The spectroscopic stability method and the eigenfunction method of obtaining relative multiplet strengths are given a convenient formulation; and values are computed for $n{p}^{3}\ensuremath{\rightarrow}n{p}^{3}$. A root ${S}^{\frac{1}{2}}$ of the line strength is defined in such a way that it transforms like a Hermitian matrix component. This enables convenient computation of line strengths in intermediate coupling. The $J$-file sum rule is shown to hold in intermediate coupling with the same degree of generality as for the electric-dipole case. Finally, closed formulas for the magnetic-dipole strengths in $\mathrm{LS}$ coupling are given and the method of transformation to intermediate coupling is indicated.