Muonic Isotope Shifts in the Even Fe Nuclei

Abstract

Isotope shifts of the 2p~* Is muonic transition energies in 54 » 56 » 58 Fe have been measured. The results indicate that the charge radii of these isotopes vary approximately as Whereas spherical Hartree-Fock calculations can account for less than one third of the observed isotope shifts, deformed Hartree-Fock results reproduce two thirds of the observed shifts. It is suggested that the remaining discrepancy is primarily due to neglected neutron-proton residual interactions.Since studies of the rearrangement of the nuclear charge distribution in response to the addition of neutrons throughout a series of isotopes provide a stringent test of one's understanding of nuclear structure, we have undertaken a systematic investigation of muonic-atom x rays of separated isotopes in the Ni region. This region is being studied extensively with electron scattering at the University of Mainz, but there has been no thorough muonic investigation of these nuclei. We report here our measurements of the shifts in the 2£ 3/2^l s 1/2 and 2p 1/2 -~ ls 1/2 transition energies for the isotopes 54 » 56 » 58 Fe, along with the results of various Hartree-Fock (HF) calculations of the charge densities of these isotopes. The present results are especially interesting in that they suggest the importance of neglected degrees of freedom in current HF theory. Results on other nuclei in this region will be published separately, along with a full description of our experimental arrangement.The measurements were performed at the Clinton P. Anderson Meson Physics Facility muon channel 1 using isotopically separated Fe 2 O s targets. Data were obtained using a coaxial Ge(Li) detector (full width at half-maximum 1. 8 keV at 1. 3 MeV) in combination with a conventional muon telescope and tar get-identification scintillator arrangement to identify x rays from the three simultaneously measured Fe isotopes. X-ray data from each target were stored separately using an on-line computer. A highly stable, computercontrolled pulser was used for gain stabilization during the runs. Calibration of the Ge(Li) spectrometer was derived from a 60 Co spectrum, which was accumulated during the data run at a rate proportional to the instantaneous intensity of the muon beam. The effect of gain shifts arising from the pulsed (6% duty cycle) nature of the muon beam were thus minimized.The centroids of the 2p-ls lines were determined by least-squares fitting the data with a Gaussian line shape. The fitting procedure took into account the known isotopic impurities of the targets. The probable effect of a reasonable variation in the impurity ratios on the final quoted energies was estimated from a series of fits to the data. The contribution of this uncertainty, less than 8 eV in all cases, is included in the quoted errors. Possible geometrical effects of relative 535

Nuclear Coulomb energies

“…Coulomb displacement energies between members of isobaric multiplets with A = 5-40 were also considered and compiled by Cerny (1968). Other previous compilations of Coulomb displacement energies are those of Sherr (1967) for ground states of A = 33-65, Harchol et aZ(1967) for ground states of A = 3-145, Long et aZ(l966) for ground states plus excited states of A = 69-145, and Sherr et aZ(1965) for ground states of A = 33-65. It should be emphasised that in most cases Coulomb displacement energies are known today to an accuracy of better than 1%.…”

Coulomb energies and nuclear radii in the energy density formalism

“…These values of A r are significantly smaller than the predictions of Hartree-Fock calculations. It is most interesting to note that recent Hartree-Fock calculations of the isotope shifts of rp in Cr, Sn and Fe isotopes, result [20][21][22] with values which are consistently smaller by ~ 30 % than the experimental values, thus indicating a possible neglection of some neutron-proton residual interaction. This missing neutron-proton residual interaction may explain the enhancement of Vz(r) at the surface required in the present study (see also Ref.…”

“…Turning to the T~= -T end of the isobaric multiplet and neglecting the additional Coulomb interaction due to the N-Z extra protons, we expect, by symmetry, the compression of the proton core relative to that of 4~ by the same amount of Arp =Ar,=0.10fm. Using a linear interpolation we find using (22), that the core of the analogue state is compressed by Ar~=0.012fm relative to the parent state (4SCa). Taking into account the Coulomb interaction of the extra proton, there should be a reduction in this A r~ as indeed obtained in the present variational calculation (for r,,-rp=0.08 fm we find Arc=0.010fm ).…”

“…At this point it is interesting to note the accumulating experimental evidence on deficiencies in current Hartree-Fock calculations regarding rms radii of proton (rv) and neutron (r,) distributions. Calculations for the even isotopes of Cr, Sn and Fe result [20][21][22] with values for the isotope shifts of r v which are consistently smaller by ~ 30 ~o than the experimental values. Also Hartree-Fock calculations with Skyrme type of effective interaction [23], produce values for the isotope shift of rp for 48Ca-4~ which are much larger than the experimental value of -0.01 fro.…”

“…For heavier nuclei this procedure relies on the linear interpolation (22) which leans on (Z*,N*), a nucleus that may be remote from stability. However, the interpolation is always by one unit only and the coefficient of the second term in (22) decreases as N-Z increases, so that the interpolation is over relatively shorter distances for heavier nuclei. It is, therefore, reasonable to expect it to be fairly reliable.…”