| Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics |
CENTRE FOR PHOTONUCLEAR EXPERIMENTS DATA |
|
Electronic Chart of Deformation gives to one possibility to obtain in comfortable form (analogous to that of well-known Charts of the Nuclides) numerical information for various nuclear deformation parameters (quadrupole moment Q and quadrupole deformation parameter b2) for ground states of many nuclei and contains the data from three sources:
Intrinsic quadrupole moment of evenly charged ellipsoid can be described by equation Q0 = 2/5 Z (b2 - a2),
where b is large, and a is small ellipsoid axises. Since quadrupole deformation parameter δ (degree of nucleus shape difference from sphere) can be written as δ = 0.3 (b2 - a2)/2<r>2,
where average mean-squared charge distribution radius is equal to <r2> = (b2 + 2a2)/5,
equation (1) would be the following Q0 = 4/3 Z <r2> δ.
Hense, using experimental quadrupole moment values the nucleus quadrupole deformation parameter values δ could be calculated by the formula δ = 0.75 Q0 /(Z <r2>).
Moment Q0 values were recalculated from static electric quadrupole moment Q values measured in laboratory system. It was supposed than near spherical nucleus shape vibrations amplitude is small in comparison to nucleus equilibrium deformation and therefore the equation Q = Q0 (3K2 - I(I + 1))/((I + 1)(2I + 3)),
where I is spin of state studied - the member of rotational band based on nucleus ground state, K is I's projection on symmetry axis (the joint characteristics of all band members). Value of <r2> was evaluated using the following expressions <r2> = 0.6R02(1 + 10/3(p a0/R0)2)/(1 + (p a0/R0)2) (Ŕ ≤ 100),
<r2> = 0.6(1.2 A1/3)2 (Ŕ > 100),
which takes into account effects of light nuclei surface diffusion properties. Parameters of radial Woods-Saxon potential form-factor (R0 = 1.07A1/3 fm and a0 = 0.55 fm)
were obtained from the data on fast electrons scattering. from the value of reduced transition probability B(E2) for (0+ ® 21+) transition. Nucleus quadrupole deformation parameter was obtained using the following equation b2 = (4p /3 Z R02)[B(E2; 0+® 21+)/e2]1/2,
where B(E2; 0+®21+) is reduced probability for Ĺ2- transition from ground 0+ to first excited 2+1 state and R02 = (1.2 A1/3 sm)2. δ ≈ 0.95b2.
Default the data from all information sources used are presented; if it is needed the data presentation of any type could be switch out using the buttons of panel displayed under the Chart. The four scales are used in the Chart, the panel “Fast Search” is intended to mark the proton number Z and neutron number N for concrete nucleus looked for. With the aim of simplifying of searching and identification of data for looked for nucleus (or nuclei group) the special colors are used (in a manner similar to that for traditional geographical maps) - brown (“mountains”) - for nuclei with positive deformation, blue (“oceans”) - negative, and green (“plains”) - for nuclei with unknown sign of deformation or with zero deformation. 5 color intensity degrees identify the parameter of deformation absolute values – more intensive color corresponds to larger value. After the click on the looked for nucleus Chart element using the smallest Chart scale all quadrupole moment Q and quadrupole deformation parameter b2 values correspondent to marked before information source (sources) together with data for energy and spin-parity for correspondent nucleus levels are presented in the additional window.
If you have any questions, comments, and/or suggestions, please, contact
CDFE Head: Vladimir V. Varlamov © Programming by
S.Yu.Komarov
, 2006
|