QUADRUPOLE MOMENTS OF THE 12+ STATES IN 206Pb AND 200Pb *

QUADRUPOLE MOMENTS OF THE TWELVE PLUS STATES IN TWO HUNDRED SIX POLYBIUM AND TWO HUNDRED POLYBIUM

The static quadrupole interaction of the twelve plus isomers in two hundred six, two hundred POLYBIUM has been measured in solid MERCURY. The quadrupole moments of the twelve plus states indicate an increase in deformation with increasing number of neutron holes.

Near the two hundred eight POLYBIUM doubly closed shell nucleus many isomeric states are known with spins from four to thirty which are, in most cases, associated with a unique quasiparticle structure. For most of these states the magnetic moments could be determined yielding information on the magnetic moment operator as well as on the structure of these states. However, magnetic moments are rather insensitive to admixtures of collective modes. The theoretical analysis of the yrast states in two hundred four POLYBIUM and TWO ONE TWO RADIUM indicates that a small core deformation has to be introduced to understand the energies of high-spin states in this mass region. In the present letter we report on the first in-beam observation of static quadrupole interactions of POLYBIUM isomers and on a substantial increase in the quadrupole moments of the TWELVE PLUS isomers between two hundred six POLYBIUM and two hundred POLYBIUM.

Experimentally, the measurement of the quadrupole interaction of high-spin isomeric states is quite challenging since the basic interaction frequency (m-sub-level splitting) decreases quadratically with the nuclear spin. One therefore needs a host which provides an electric field gradient sufficiently high to induce a measurable sublevel splitting, such as for example solid MERCURY may play the same important role in determining quadrupole moments as did liquid MERCURY in determining magnetic moments especially in the POLYBIUM region. We have therefore measured the quadrupole interaction of several isomers in different POLYBIUM isotopes, among them the TWELVE PLUS i sub one three half to the power of negative two states in two hundred POLYBIUM and two hundred six POLYBIUM using solid MERCURY as host.

The determination of nuclear moments, especially quadrupole moments, by "in-beam" techniques such as perturbed angular distributions used in the experiments reported here can be hampered by damage of the lattice near the final site of the excited nucleus under study. POLYBIUM offered the advantage that the "in-beam" procedure could be checked easily by means of the well-known isomeric FOUR PLUS state in two hundred four POLYBIUM. Consequently, we have studied the FOUR PLUS state both “in-beam” and in the radioactive decay of the one hour activity of two hundred four POLYBIUM M.

The isomeric states were populated and aligned by the ALPHA minus TWO HUNDRED sixty particle beam from the tandem accelerator at the Chalk River Nuclear Laboratories. For the “in-beam” study of the FOUR PLUS states in two hundred four POLYBIUM an energy of was chosen, while the radioactive source was produced at E sub ALPHA equals twenty-eight. The targets consisting of MERCURY enriched in the required MERCURY isotopes were prepared by placing a drop of liquid MERCURY into a small shallow hole cut in a COPPER plate which was then mounted onto a Joule-Thomson cryo-tip and cooled below the melting point of MERCURY.

The quadrupole modulation was measured by using the standard perturbed angular distribution method. Time spectra were derived for various GAMMA rays observed with GE(LI) detectors placed at ZERO degrees and NINETY degrees with respect to the beam direction. The background corrected ratio of the GAMMA ray intensities then yields the quadrupole modulation pattern which depends on the spin, the quadrupole coupling constant E squared Q Q over H, the symmetry of the E F G (axially symmetric for Hg) and the spatial orientation and distribution of the E F G (e.g. oriented in a single crystal or randomly oriented in a polycrystal). For high-spin states especially, the proper orientation of the single-crystal axis can be very helpful in determining the quadrupole coupling constant unambiguously. As it turned out, our target preparation technique favoured the crystallization of Hg in large grains. Although possible in principle, we did not find it necessary to take special measures to ensure the growth of a single crystal or to orient it, but rather determined the crystal orientations by fitting the observed time spectra I of theta T. In the case of two hundred six Pb three gamma-ray transitions could be employed to observe the quadrupole modulation pattern, the twelve to the power of plus E three transition E subscript gamma equals one thousand three hundred sixty-nine kilo Electron Volts, the ten to the power of plus E one transition E subscript gamma equals one thousand two hundred ninety-nine kilo Electron Volts and the nine to the power of minus E two transition E subscript gamma equals four hundred fifty-eight kilo Electron Volts while in two hundred Pb the only suitable transition was the ten to the power of plus E one transition E subscript gamma equals seven hundred seventy-seven kilo Electron Volts. Fig. one shows the modulation spectra observed for the twelve to the power of plus states in two hundred six Pb and two hundred Pb, respectively. The patterns are basically different reflecting the fact that the one hundred ninety-eight Hg target two hundred Pb solidified mainly in the form of a large grain with the c-axis perpendicular to the beam and gamma y-detection plane, while the two hundred four Hg target two hundred six Pb formed a crystal with the c c-axis in the plane perpendicular to the ninety-degree-detector axis and with an angle of roughly fifty degrees to the beam direction. The values for the quadrupole coupling constant E squared Q Q over H, extracted from the modulation patterns are two hundred one point six (eight) megahertz for the twelve to the power of plus state in two hundred six Pb and three hundred twenty-two point eight (sixteen) for the twelve to the power of plus state in two hundred Pb. Since the two coupling constants were measured at different temperatures the temperature dependence of the E F G had to be determined. This was obtained from the measurement of the coupling constant of the four to the power of plus state in two hundred four Pb.

between T equals eighty-two and two hundred two K yielding E squared O Q over H of T equals two hundred twenty-four point five (ten) one minus seven point six (two) times ten to the power of negative five T to the power of three halves megahertz. Applying the correction for temperature dependence, we then obtain for the ratio of the quadrupole moments of the two twelve to the power of plus isomers absolute value O of two hundred P subscript b, twelve plus over O of two hundred six P subscript b, twelve plus equals one point five five three (ten).

Although the understanding of electric field gradients in metals, especially in sp-metals, has improved considerably, it is not yet good enough to deduce quadrupole moments from the measured coupling constant reliably. However, from the extensive studies, both experimentally and theoretically, on single-particle levels and effective charges in the lead region by the Stockholm group it can be concluded that the isomeric one two plus and the ten plus states in two hundred six lead are rather pure members of the left parenthesis I thirteen over two right parenthesis to the power of negative two multiplet. Therefore, the quadrupole moment of this one two plus state can be derived from the known B left parenthesis E two right parenthesis value of the one two plus to ten plus transition by using angular momentum algebra, absolute value of E Q left parenthesis one two plus right parenthesis equals ten point three eight left bracket B left parenthesis E two, one two plus to ten plus right parenthesis right bracket to the power of one half, which yields absolute value of Q left parenthesis two hundred six P B, one two plus right parenthesis equals fifty-one left parenthesis two right parenthesis femto meters squared. The error reflects only the experimental error of the B left parenthesis E two right parenthesis value. This procedure is well justified for two-particle hole states in the lead region, since the experimental transition moment B left parenthesis E two, eight plus to six plus right parenthesis in two hundred ten polonium agrees with the one calculated from the static moment Q left parenthesis two hundred nine right parenthesis thirty-one, H nine over two ground state within an error of about ten percent.

The derived quadrupole moment can now be used for calibrating the electric field gradient of lead in mercury, resulting in a value of E Q equals sixteen point three left parenthesis seven right parenthesis times ten to the power of seventeen volts per square centimeter at T equals two hundred two kelvin. That the E F G, at least in this temperature range, is not influenced by any kind of damage or other effects associated with the in-beam observation was proved by finding agreement within experimental errors for the coupling constant of the four plus state in two hundred four lead obtained in-beam and in the radioactive source experiment. From the measured ratio and with the calibration of the E F G from the one two plus state in two hundred six lead we derived for the moment of the one two plus state in two hundred lead absolute value of Q left parenthesis two hundred P B, one two plus right parenthesis equals seventy-nine left parenthesis three right parenthesis femto meters squared. This rather large increase in the quadrupole moment indicates that two hundred lead can no longer be described by highly pure single-particle wavefunctions, but rather one has to consider additional collective effects. A similar increase is already observed in the B left parenthesis E two right parenthesis value of the one two plus to ten plus transition in two hundred lead as compared to two hundred six lead. Although the exact transition energy is not known it is assumed to be below fifty kiloelectronvolts in the recent compilation of Schmorak the B left parenthesis E two right parenthesis value can be derived from the half-life within about ten percent since the transition energy dependence is roughly balanced by the energy dependence of the conversion coefficient. In table one the B left parenthesis E two right parenthesis values quoted for the one two plus to ten plus transition in two hundred, two hundred six lead are based on the more accurate data obtained for the half-lives in this experiment.

Assuming that the relationship between the quadrupole moment and the B left parenthesis E two right parenthesis value still holds, one calculates from the transition rate a quadrupole moment for two hundred lead of absolute value of Q sub cal left parenthesis two hundred P B, one two plus right parenthesis equals seventy-eight left parenthesis four right parenthesis femto meters squared, in close agreement with the value derived from the experimental ratio. This indicates that the one two plus and the ten plus state are influenced in a similar way. The increase in both the quadrupole moment and the B left parenthesis E two right parenthesis value might be understood in terms of an increasing contribution from proton excitations. These excitations become more likely with increasing deformation which is suggested from the fact that the one one three over two shell comes closer to the Fermi surface at slightly prolate deformation. Using the simple relationship between intrinsic moment and the deformation one derives a deformation parameter for two hundred lead absolute value of beta approximately zero point zero three rather similar to the one Andersson et al. had to use for states around omega equals twelve to calculate the yrast states of two hundred four lead.

Since the one two plus states in lead isotopes are known to be isomeric over a wide range in mass numbers it will be interesting to determine their quadrupole moments to study the influence of the increasing number of neutron holes on the deformation.