Effective hyperfine Hamiltonian in homonuclear diatomic molecules. Application to the B state of molecular iodine

Abstract

The effective hyperfine Hamiltonian is studied in the case of homonuclear diatomic molecules, using irreducible tensorial algebra. The second order perturbation terms due to the magnetic dipole and electric quadrupole Hamiltonian are calculated in a compact form. These calculations are applied to the B state of molecular iodine : the experimental values of the scalar and tensorial spin-spin coupling constants are interpreted. Moreover it is shown that the recently published magnetic octupole coupling value for the B state is unrealistic and also that some other terms must be introduced in the hyperfine Hamiltonian

Global analysis of data on the spin-orbit-coupledA1Σu+andBai1, Ahmed2, Beser3 et al. 2011Phys. Rev. A

“…[89] corrected errors in the Hamiltonian matrix of [88] and also in the forms adapted from [90]. An alternative formalism developed by [91], originally intended for application to the I 2 molecule, was applied to the b 3 Π u state of Na 2 by [37]. Later, [92], from observations of the 1 3 ∆ g state of Na 2 , and [93], from data on mixed A 1 Σ + u and b 3 Π u states of Na 2 , found that their observations could be explained almost entirely by the Fermi-contact parameter alone.…”

LIF measurement of the vibrational dependence of the N2(B 3Π g ) hyperfine splitting parameters

“…A total of about 500 rotational lines were measured in the (5,1), (10,6) and (17,15) a The standard deviation of the last digits is given in parentheses…”

“…The numerical analysis was greatly facilitated by auto-QI~ (8) (10,6) band of the Ne(B--A) system is shown, as scanned with the resolution of [4] (left) and with the improved resolution of the present work (right). The bottom trace gives the frequency markers from a calibrated interferometer matic measurement of the peak wavelength of each hfs component.…”

“…The magnetic coupling parameters involve certain averages over the electronic wave functions of the open shells only. For the constants Kaa, DI~, DI-~ and G~a, in the notation of [6], these relationships have been given in (42)-(55) of [4]. They are summarized in Table 3, col. 2.…”

“…Finally G~ is the parameter of the nuclear spinelectron orbital magnetic moment coupling and is proportional to the integral 14 . As is typical of magnetic dipolar interactions, I 2 to 14 contain a 1/r 3 term. The complete numerical factors between the integrals I, and the corresponding constants are given in [4], based on the SI system of units as in [6]. An equivalent notation for the first two constants was used in [1,2]: c~ and fl are also related to the integrals I~ and I2, respectively, according to (18) and (20) in [1] (based here on the electromagnetic system).…”