$\alpha$-cluster structure of ${}^{18}\mathrm{O}$

Background: Clustering phenomena in $N\ne Z$ nuclei provide an opportunity to understand the interplay between cluster and nucleon degrees of freedom.

Purpose: To study resonances in the ${}^{18}\mathrm{O}$ spectrum, populated in ${}^{14}\mathrm{C}+\alpha$ elastic scattering.

Method: The thick target inverse kinematics technique was used to measure the excitation function for the ${}^{14}\mathrm{C}+\alpha$ elastic scattering. A 42-MeV ${}^{14}\mathrm{C}$ beam was used to populate states of excitation energy up to 14.9 MeV in ${}^{18}\mathrm{O}$. The analysis was performed using a multilevel, multichannel $R$-matrix approach.

Results: Detailed spectroscopic information, including spin parities, partial $\alpha$- and neutron-decay widths and dimensionless reduced widths, was obtained for excited states in ${}^{18}\mathrm{O}$ between 8 and 14.9 MeV in excitation energy. Cluster-nucleon configuration interaction model calculations of the same quantities are performed and compared to the experimental results.

Conclusions: Strong fragmentation of large $\alpha$-cluster strengths is observed in the spectrum of ${}^{18}\mathrm{O}$, making the $\alpha$-cluster structure of ${}^{18}\mathrm{O}$ quite different from the pattern of known quasirotational bands of alternating parity that are characteristic of $N=Z$, even-even nuclei like ${}^{16}\mathrm{O}$ and ${}^{20}\mathrm{Ne}$.

Figure 1

Inversion doublet, $\alpha$-cluster quasirotational bands for ${}^{16}\mathrm{O}$ and ${}^{20}\mathrm{Ne}$. All of the unbound states within the bands have large $\alpha$-reduced widths. The solid curves connect the positive-parity states, while the dashed lines connect the negative-parity states. Blue and red color coding correspond to ${}^{20}\mathrm{Ne}$ and ${}^{16}\mathrm{O}$, respectively.

Figure 2

Experimental setup for measurements of the elastic scattering of ${}^{14}\mathrm{C}$ by $\alpha$ particles using the TTIK technique. The silicon detectors were placed at angles ranging from $0^{\circ }$ to ${60}^{\circ }$ in steps of $5^{\circ }$. Only the extreme angles are shown.

Figure 3

Excitation function for ${}^{14}\mathrm{C}+\alpha$ elastic scattering at ${180}^{\circ }$ in the c.m. frame measured with a 42-MeV ${}^{14}\mathrm{C}$ beam. The solid curve is the best $R$-matrix fit.

Figure 4

Excitation functions for the elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ from 8 to 9 MeV with the best $R$-matrix fit (solid curve). A $3^{-}$ spin-parity assignment for the state at 8.82 MeV and a $2^{+}$ for the state at 8.96 MeV were used for this diagram.

Figure 5

Excitation functions for the elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ with the best $R$-matrix fit (solid curve) for the energy range of 9–10 MeV. The dashed and the dash-dotted curves represent the best $R$-matrix fit without the inclusion of the $1^{-}$ and $2^{+}$ resonances at 9.76 and 9.79 MeV, respectively

Figure 6

Excitation functions for elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ at ${180}^{\circ }$, ${147}^{\circ }$, and ${115}^{\circ }$ with the best $R$-matrix fit (solid curve) for the energy range of 10–11 MeV. The dashed line and the dash-dotted curve represents the best $R$-matrix fit without the inclusion of the $2^{+}$ and $1^{-}$ states at 10.42 and 10.80 MeV, respectively.

Figure 7

Excitation functions for elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ at ${180}^{\circ }$, ${150}^{\circ }$, and ${120}^{\circ }$ with the best $R$-matrix fit (solid curve) for the energy range of 11–12 MeV. The dashed line represents the $R$-matrix fit without the inclusion of a $2^{+}$ state at 11.31 MeV.

Figure 8

Excitation functions for elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ at ${180}^{\circ }$, ${156}^{\circ }$, and ${131}^{\circ }$ with the best $R$-matrix fit (solid curve) for the energy range of 12–13 MeV.

Figure 9

Excitation functions for elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ at ${180}^{\circ }$, ${160}^{\circ }$, and ${140}^{\circ }$ with the best $R$-matrix fit (solid curve) for the energy range of 13–14 MeV.

Figure 10

Excitation function for elastic scattering of $\alpha$ particles from ${}^{14}\mathrm{C}$ at ${180}^{\circ }$, ${163}^{\circ }$, and ${145}^{\circ }$ with the best $R$-matrix fit (solid curve) for the energy range of 14–14.9 MeV.

Figure 11

Total cross section for the ${}^{14}\mathrm{C}(\alpha ,n)$ reaction taken from Refs. [30] and [37], where absolute normalization was not performed. The solid curve corresponds to the $R$-matrix calculation with resonance parameters from the fit to the ${}^{14}\mathrm{C}(\alpha ,\alpha )$ data. The $R$-matrix prediction was used to normalize the data here.

Figure 12

Distribution of $\alpha$ strength by spin parity. Solid blue bars are the states observed in this work and the hatched red bars are the predictions of the CNCIM. The lengths of the bars correspond to the experimental dimensionless reduced $\alpha$ (solid blue bars) or the calculated ${\mathrm{SF}}_{\alpha }$ (hatched red bars). The black lines represent known bound or very narrow near-threshold states. The length of the black line is set to the calculated ${\mathrm{SF}}_{\alpha }$ of the corresponding CNCIM state. The suggested association between the states observed in this work and those predicted by CNCIM calculations is indicated by connecting lines. States with $\alpha$ strength below 2% are ignored, except for the few cases for which association between the CNCIM and the experimental state is suggested.

Figure 13

Phase shifts for $0^{+}$ (top) and $2^{+}$ (bottom) states in ${}^{18}\mathrm{O}$ from potential model (dash-dotted curve) and $R$-matrix (solid line) calculations