Partial conservation law in a schematic single j shell model

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.

Characterization of the shallow state of iodine chloride

A weakly bound Ω = 1 state of ICl, [Formula: see text], which converges to the ground state 1(2P3/2) + Cl(2P3/2) of the separated atoms, has been identified and characterized. Spectroscopic constants of this state are Te = 17 338.0(13), ωe = 32.85(48), ωexe = 1.272(40), 103Be = 38.2(13), 104αe = 8.89(34), 105γe = −8.1(20) cm−1, and re = 4.01(6) Å. The dissociation energy De = 219.6 cm−1 is consistent with the value predicted for a Morse function, [Formula: see text]. Transitions [Formula: see text] are allowed owing to homogeneous coupling between ã and the well-defined A(3π1) state; in fact, at medium-long range (r = 6–6.5 Å, D–Gν = 20–30 cm−1), the diabatic ã and A curves cross at a small angle. Principal features of the crossing are explained if the electronic interaction matrix element is ca. 4 cm−1, corresponding to weak coupling. Heterogeneous perturbations of the A and ã states in the range D–Gν < 200 cm−1 are attributed to coupling with high vibrational levels of the ground state X(1Σ+).

Rotational analysis and deperturbation of the C2Σ+–X2Σ+ band systems of BeH and BeD

A new C2Σ+–X2Σ+ transition of BeH and BeD is observed in a beryllium are in hydrogen or deuterium gas mixed with argon. The rotational analysis of the most intense of these strongly red degraded bands, which involve ν′ = 0–2 for BeH and ν′ = 0 for BeD, allows one to derive molecular constants for the new C2Σ+ state. The latter has a large internuclear equilibrium distance (re = 2.301 Å) and a shallow potential energy minimum [Formula: see text]. The principal molecular constants determined are:C2Σ+Tc = 30 953.94 cm−1[Formula: see text]Rotational perturbations between the C2Σ+ and A2Π states are observed in the C–X bands of BeH and BeD and in two new A–X bands of BeH (4–4 and 5–5) which have also been observed and analyzed. These perturbations are treated by a matrix approach and yield a value for the interaction matrix element [Formula: see text].The C–X bands analyzed involve the higher vibrational levels of the X2Σ+ state and allow, therefore, a substantial improvement of the ground state molecular constants to be made and a good Rydberg–Klein–Rees (RKR) potential energy curve to be calculated. The limiting curve of the predissociation confirms the previous value of the dissociation energy [Formula: see text] and indicates that a small maximum, less than 200 cm−1, could exist at [Formula: see text] in the ground state potential energy curve.Franck–Condon factors for the C2Σ+–X2Σ+ bands of BeH and BeD are also calculated.

Some Hartree–Fock Results for (3d + 4s)q+1 Configurations

Self-consistent field calculations have been performed in three different ways for the average energy of the configurations 3dq−14s2, 3dq4s, and 3dq+1, q = 2,3,..., 9 of the neutral atoms scandium to nickel. The calculations differ in the way the radial functions depend on the configuration. Parameters which enter into the interaction matrix for states of these configurations are reported. It is shown that the lack of orthogonality of an orbital from one configuration with that of another may alter the interaction matrix element significantly, and that the parameters for radial functions independent of the configuration are significantly different from those that depend on the configuration.