From Coulomb excitation cross sections to nonresonant astrophysical rates in three-body systems: The ${}^{17}\mathrm{Ne}$ case

Coulomb and nuclear dissociation of ${}^{17}\mathrm{Ne}$ on light and heavy targets are studied theoretically. The dipole E1 strength function is determined in a broad energy range including energies of astrophysical interest. Dependence of the strength function on different parameters of the ${}^{17}\mathrm{Ne}$ ground-state structure and continuum dynamics is analyzed in a three-body model. The discovered dependence plays an important role for studies of the strength functions for the three-body E1 dissociation and radiative capture. The constraints on the $\left[s^2\right]/\left[d^2\right]$ configuration mixing in ${}^{17}\mathrm{Ne}$ and on $p$-wave interaction in the ${}^{15}\mathrm{O}$+$p$ channel are imposed based on experimental data for ${}^{17}\mathrm{Ne}$ Coulomb dissociation on heavy target.

Figure 1

The level schemes of ${}^{17}\mathrm{Ne},{}^{16}\mathrm{F}$ and the coordinate systems for three-body representation of ${}^{17}\mathrm{Ne}$ used in this work. Arrows in the upper panel illustrate the processes of astrophysical relevance: (i) direct resonant $2p$ capture via the first excited $3/2^{-}$ state of ${}^{17}\mathrm{Ne}$ and (ii) direct two-step nonresonant capture via soft dipole mechanism (SDM, $1/2^{+}$ and $3/2^{+}$ quantum numbers) with strength functions peaked above 3.5 MeV.

Figure 2

Decompositions of the E1 strength function over partial contributions. The calculations are done with $V_p=-21$ MeV and the ${}^{17}\mathrm{Ne}$ g.s. WF with $\approx 50\%$ of the $\left[s^2\right]$ configuration.

Figure 3

The eikonal model cross sections of the nuclear, E1 nuclear, and E1 Coulomb dissociation on the lead target for 500 A MeV ${}^{17}\mathrm{Ne}$ beam as function of the impact parameter $b$ are shown opposite left axis by the solid, dotted and dashed curves, respectively. The contribution of the ${}^{17}\mathrm{Ne}$ low excitation energy region to the E1 Coulomb cross sections is illustrated by the dash-dotted curve. Calculations are done with $V_p=-21$ MeV and ${}^{17}\mathrm{Ne}$ g.s. WF with $\approx 50\%$ of the $\left[s^2\right]$ configuration. The absorption function $F_{\text{abs}}\left(b\right)$ is shown opposite right axis by the thick gray line.

Figure 4

Dependence of E1 strength function in ${}^{17}\mathrm{Ne}$ g.s. on different parameters of the nuclear structure up to energy of several MeV. (a) Variation of the ${}^{17}\mathrm{Ne}$ g.s. binding energy. (b) Position of the low-lying $s$-wave resonance in ${}^{15}\mathrm{O}$+$p$ channel (the g.s. energy of the ${}^{16}\mathrm{F}$, which is a two-body subsystem of ${}^{17}\mathrm{Ne}$). (c) Interaction in the $p$-wave of the ${}^{15}\mathrm{O}$+$p$ channel; see Eq. (16) for parameter $V_p$. (d) The $\left[s^2\right]/\left[d^2\right]$ ratio in the ${}^{17}\mathrm{Ne}$ g.s. WF: $100\%$ of $\left[s^2\right]$ vs. $100\%$ of $\left[d^2\right]$.

Figure 5

Sensitivity of E1 strength function in ${}^{17}\mathrm{Ne}$ g.s. to different aspects of nuclear structure at low energies. Panels are the same as in Fig. 4 but for extremely low energies (log scales).

Figure 6

The phase shifts in the $p$-wave of the ${}^{15}\mathrm{O}$+$p$ channel for different $V_p$ parameters.

Figure 7

Measured EMD cross sections (lead target [10]) and those calculated with different potentials in the $p$-wave state in the ${}^{15}\mathrm{O}$+$p$ channel. The blue dotted curves correspond to the contribution of the $50\%\left[s^2\right]$ configuration of the ${}^{17}\mathrm{Ne}$ g.s., while the red dashed curves correspond to the contribution of the $50\%\left[d^2\right]$ configuration. Two black solid curves are the upper and lower limit weighted sums of $\left[s^2\right]$ and $\left[d^2\right]$ fitting the experimental data. Note varying vertical scales.

Figure 8

Measured EMD cross sections and the one calculated with $V_p=-40$ MeV for potentials in the $p$-wave state in the ${}^{15}\mathrm{O}$+$p$ channel for a lead target. The illustration of transition from SDM character of E1 strength function in Fig. 7 to that generated on real resonant states. The weighted sum (black curve) supposes practically no contribution from the $\left[s^2\right]$ configuration to fit the data.

Figure 9

The upper and lower limit weights of the $\left[s^2\right]$ configuration as obtained in the fits of Fig. 7 with different $p$-wave interactions in the ${}^{15}\mathrm{O}$+$p$ channel. The hatched ranges correspond to admissible $\left[s^2\right]$ weights.

Figure 10

Black and grey histograms show the Monte Carlo results for angular distribution in the “T” Jacobi system for $\left[s^2\right]\to \left[sp\right]$ and $\left[d^2\right]\to \left[dp\right]$ transitions correspondingly. Case $V_p=-21$ MeV. Panels (a) and (b) correspond to left slope and peak region of the SDM strength function.

Figure 11

Comparison of the theoretical E1 strength functions from Refs. [6, 36] converted to Coulomb dissociation cross sections by Eq. (10) in linear (a) and logarithmic (b) scale. The diamonds shows the data (lead target) of Ref. [10].

Figure 12

Astrophysical radiative capture rate for the ${}^{15}\mathrm{O}$+$p$+$p\to {}^{17}\mathrm{Ne}$+$\gamma$ reaction. The results of this work are compared with of our previous work [7] and Ref. [37].

Figure 13

Astrophysical radiative capture rate for the ${}^{15}\mathrm{O}$+$p$+$p\to {}^{17}\mathrm{Ne}$+$\gamma$ reaction. The results of this work are compared with Ref. [6].