The sizes of 1p shell nuclei

doi:10.1016/0029-5582(66)90133-7

Nuclear Physics

Volume 85, Issue 1, September 1966, Pages 97-113

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Abstract

Data on electron scattering, proton binding energies and Coulomb energies in nuclei of the 1p shell are analysed to give information on the nuclear size. The simplest model, a spherically symmetrical, velocity-independent potential of Saxon-Woods form is used; it is found that the parameters characterizing the nuclear size are essentially the same as deduced by the three methods and that there is no significant change in nuclear size through the shell. If we use a diffuseness parameter of a = 0.5 fm, the following quantities cover the entire shell: $〈r^{2} 〉_{m}^{12} = 2.32±o.14 fm$ ; R = 2.94±0.20 fm; V₀ = 61±6 MeV; the rms radius refers to neutrons and protons taken together and all quantities are in the centre-of-mass system.

References (5)

U. Meyer-Berkhout et al.
Ann. of Phys.
(1959)
L.R.B. Elton
Nuclear sizes
(1961)

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1979, Nuclear Physics, Section A
Angular distributions of elastically scattered ³He particles from the 1p shell nuclei ⁶Li, ⁷Li, ⁹Be, ¹⁰B, ¹¹B, ¹²C and ¹⁶O were measured by using a 45 MeV ³He beam. The absolute differential cross section data obtained were analysed in terms of the standard optical model. Using the fact that the rms radius of the 1p shell nuclei is nearly constant a simple folding model allows finding an optical potential family whose real potential depth varies linearly with the target mass. The best fits exhibit a normalized volume integral of about 400 MeV · fm³ for the real potential. From the best-fit parameters a mean parameter set is deduced which varies smoothly with the target mass A_T. The average parameter set compares well with the systematics found for heavier nuclei.
Isospin mixing between T=0 and 1 states in the 1p-shell
1978, Physics Letters B
The effect of using different proton and neutron wave functions to evaluate matrix elements of a charge independent nucleon-nucleon interaction is examined. It is shown that this is predominantly an isovector effect and in the 1p-shell can give rise to large off diagonal matrix elements (⪆ 100 keV). The magnitude of these matrix elements are extremely sensitive to the detailed structure of the single particle wave functions. Until this effect is satisfactorily taken into account it will be difficult to demonstrate the need for a change symmetry breaking nucleon-nucleon interaction from a measurement of isospin mixing between T=0 and 1 states.
Calculation of odd and doubly odd nuclei with skyrme-type forces
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Magnetic elastic electron scattering from 3Be and 13C
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Elastic scattering through 180° from ⁹Be, ¹²C and ¹³C targets has been observed for electrons of 35 to 90 MeV. Magnetic scattering cross sections for ⁹Be and ¹³C have been obtained by subtracting charge scattering as deduced from the scattering from the spin-zero nucleus ¹²C. Theoretical shell model predictions for the magnetic cross sections are derived for (1s)⁴(1p)^A−4 configurations and various coupling schemes. Both harmonic oscillator and Woods-Saxon radial wave functions are used. A comparison of our results with magnetic cross sections calculated in DWBA yields magnetic rms radii $〈r^{2} 〉_{M}^{12} = 3.2 ± 0.3 fm$ and $〈r^{2} 〉_{M}^{12} = 3.3 ± 0.3 fm$ for ⁹Be and ¹³C. For ¹³C a combined flt to our low-q data and to earlier high-q data, yields $〈r^{2} 〉_{M}^{12} = 3.4 ± 0.1 fm$ and a strong preference for intermediate coupling (IC) wave functions. Magnetic dipole scattering from ⁹Be is also close to the IC prediction, as deduced from a fit to our data and earlier high-q data. The fitted value of the octupole moment $Ω = 5±1 μ_{Nfm}^{1}$ can only be explained by a deformation of the average nuclear potential. The radial size $〈r^{2} 〉_{1p}^{12} = 2.85 ± 0.05 fm$ for the 1p radial wave function is in agreement with both the ⁹Be and ¹³C data.
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^†: Now at the University of Zambia.

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Nuclear Physics

Abstract

References (5)

Ann. of Phys.

Nuclear sizes

Cited by (32)

Optical model analysis of <sup>3</sup>He elastic scattering from s-d shell nuclei at 25 MeV

Optical model analysis of the elastic scattering of 45 MeV <sup>3</sup>He particles on 1p shell nuclei

Isospin mixing between T=0 and 1 states in the 1p-shell

Calculation of odd and doubly odd nuclei with skyrme-type forces

Magnetic elastic electron scattering from <sup>3</sup>Be and <sup>13</sup>C

Exchange effects in the <sup>7</sup>Li(<sup>3</sup>He, α)<sup>6</sup>Li reaction