Interpretation of Coulomb breakup of $^{31}\mathrm{Ne}$ in terms of deformation

Rapid Communication

Interpretation of Coulomb breakup of ${}^{31}{Ne}$ in terms of deformation

Ikuko Hamamoto

Phys. Rev. C 81, 021304(R) – Published 23 February 2010

Abstract

The recent experimental data on Coulomb breakup of the nucleus ${}^{31}{Ne}$ are interpreted in terms of deformation. The measured large one-neutron removal cross section indicates that the ground state of ${}^{31}{Ne}$ is either an $s$ halo or a $p$ halo. The data can be most easily interpreted as the spin of the ground state being 3/ $2^{-}$ coming from either the Nilsson level [ $330 1 / 2$ ] or the Nilsson level [ $321 3 / 2$ ] depending on the neutron separation energy $S_{n}$ . However, the possibility of $1 / 2^{+}$ coming from [ $200 1 / 2$ ] is not excluded. It is suggested that if the large ambiguity in the measured value of $S_{n}$ of ${}^{31}{Ne}$ , $0.29 \pm 1.64$ MeV, can be reduced by an order of magnitude, say to be $\pm 100$ keV, one may get a clear picture of the spin-parity of the halo ground state.

Received 12 December 2009

DOI:https://doi.org/10.1103/PhysRevC.81.021304

Authors & Affiliations

Ikuko Hamamoto

Division of Mathematical Physics, Lund Institute of Technology at the University of Lund, Lund, Sweden and The Niels Bohr Institute, Blegdamsvej 17, Copenhagen Ø, DK-2100, Denmark

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 81, Iss. 2 — February 2010

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The integrand of the radial integral on the right-hand side of Eq. (10) as a function of radial variable $r$ . Namely, the product (solid curve) of radial variable, the bound $2 p_{3 / 2}$ radial wave function $R_{2 p_{3 / 2}}^{(b)}$ $(ɛ = - 300$ keV, $r$ ) (dashed curve) in units of fm $^{- 1 / 2}$ , and the continuum $s_{1 / 2}$ radial wave function $R_{s_{1 / 2}}^{(c)}$ ( $ɛ = + 60$ keV, $r$ ) (dotted curve) in units of fm $^{- 1 / 2}$ MeV $^{- 1 / 2}$ . The unit of the ordinate is for the product, while the figures written along the ordinate can be used also for the radial wave functions, $R_{2 p_{3 / 2}}^{(b)}$ and $R_{s_{1 / 2}}^{(c)}$ , in respective units. The radial integration of the solid curve gives the radial matrix element of the $E 1$ transition, $2 p_{3 / 2}$ $\to$ $s_{1 / 2}$ . The depth of the Woods-Saxon potential is $- 46.75$ MeV for which the eigenstate of the $2 p_{3 / 2}$ neutron is obtained at $- 300$ keV, while the diffuseness and the radius used are 0.67 and 3.946 fm (for $A = 30$ ), respectively.Reuse & Permissions
Figure 2
Neutron one-particle levels in Woods-Saxon potentials as a function of quadrupole deformation parameter $β$ . The potential depth is approximately adjusted so that the 21st neutron of the prolately deformed nucleus ${}^{31}{Ne}$ can be a halo neutron. The depth, the diffuseness and the radius of the potential are $- 39$ MeV, 0.67 fm, and 3.946 fm (for $A = 30$ ), respectively. Positive-parity levels are plotted by solid curves, while asymptotic quantum numbers [ $N$ $n_{z}$ $Λ$ $Ω$ ] are denoted for bound levels. See the text for details.Reuse & Permissions
Figure 3
(a) Calculated probabilities of the major components of the [330 1/2] level with $β = 0.3$ as a function of energy eigenvalue $ɛ_{Ω}$ . (b) Calculated probabilities of the major components of the $[3213 / 2]$ level with $β = 0.5$ as a function of energy eigenvalue $ɛ_{Ω}$ . The potential depth is adjusted to obtain respective $ɛ_{Ω}$ values as energy eigenvalues of the deformed potential. The diffuseness and the radius of the potential are 0.67 and 3.946 fm (for $A = 30$ ), respectively.Reuse & Permissions
Figure 4
Estimate of $| \int r dr R_{p_{3 / 2}}^{(b)} (- 300 keV, r) R_{s_{1 / 2}}^{(c)} (ɛ_{c}, r) |^{2}$ on the right-hand side of Eq. (10) as a function of $ɛ_{c}$ . The solid curve is obtained by using the $p_{3 / 2}$ wave function taken from the $p_{3 / 2}$ component of the [330 1/2] level, which is bound at $- 300$ keV for $β = 0.3$ . The probability of the $p_{3 / 2}$ component is 0.5225. The dotted curve is calculated using the $2 p_{3 / 2}$ wave function with the energy eigenvalue $- 300$ keV, which is normalized to 0.5225. The depth of the Woods-Saxon potential of the former is $- 38.39$ MeV, while that of the latter is $- 46.75$ MeV.Reuse & Permissions

Physical Review C

covering nuclear physics

Interpretation of Coulomb breakup of ${}^{31}{Ne}$ in terms of deformation

Ikuko Hamamoto

Phys. Rev. C 81, 021304(R) – Published 23 February 2010

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review C

covering nuclear physics

Interpretation of Coulomb breakup of Ne31 in terms of deformation

Ikuko Hamamoto

Phys. Rev. C 81, 021304(R) – Published 23 February 2010

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Interpretation of Coulomb breakup of ${}^{31}{Ne}$ in terms of deformation