Resonant states in ${}^7\mathrm{H}$: Experimental studies of the ${}^2\mathrm{H}({}^8\mathrm{He},{}^3\mathrm{He})$ reaction

The extremely neutron-rich system ${}^7\mathrm{H}$ was studied in the direct ${}^2\mathrm{H}({}^8\mathrm{He},{}^3\mathrm{He}){}^7\mathrm{H}$ transfer reaction with a 26 $A\mathrm{MeV}$ secondary ${}^8\mathrm{He}$ beam [Bezbakh et al., Phys. Rev. Lett. 124, 022502 (2020)]. The missing mass spectrum and center-of-mass angular distributions of ${}^7\mathrm{H}$, as well as the momentum distribution of the ${}^3\mathrm{H}$ fragment in the ${}^7\mathrm{H}$ frame, were constructed. In addition, we carried out another experiment with the same beam but a modified setup, which was cross-checked by the study of the ${}^2\mathrm{H}({}^{10}\mathrm{Be},{}^3\mathrm{He}){}^9\mathrm{Li}$ reaction. A solid experimental evidence is provided that two resonant states of ${}^7\mathrm{H}$ are located in its spectrum at 2.2(5) and $5.5\left(3\right)\mathrm{MeV}$ relative to the ${}^3\mathrm{H}+4n$ decay threshold. Also, there are indications that the resonant states at 7.5(3) and $11.0\left(3\right)\mathrm{MeV}$ are present in the measured ${}^7\mathrm{H}$ spectrum. Based on the energy and angular distributions, obtained for the studied ${}^2\mathrm{H}({}^8\mathrm{He},{}^3\mathrm{He}){}^7\mathrm{H}$ reaction, the weakly populated 2.2(5)-MeV peak is ascribed to the ${}^7\mathrm{H}$ ground state. It is highly plausible that the firmly ascertained 5.5(3)-MeV state is the $5/2^{+}$ member of the ${}^7\mathrm{H}$ excitation $5/2^{+}\text{–}3/2^{+}$ doublet, built on the $2^{+}$ configuration of valence neutrons. The supposed 7.5-MeV state can be another member of this doublet, which could not be resolved in Bezbakh et al. [Phys. Rev. Lett. 124, 022502 (2020)]. Consequently, the two doublet members appeared in the spectrum of ${}^7\mathrm{H}$ in the work mentioned above as a single broad 6.5-MeV peak.

Figure 1

The ${}^7\mathrm{H}$ level scheme, and the known neighboring ${}^5\mathrm{H}$ [15, 16, 17], and ${}^4\mathrm{H}$ systems important for the discussions of this work. The solid red arrow illustrates the decay mechanism of the ${}^7\mathrm{H}$ ground state which is expected to be “true” $4n$ emission. The dotted blue arrows illustrate the decay mechanism of the higher excitations in ${}^7\mathrm{H}$, which is expected to be the sequential $\left(2n\right)+\left(2n\right)$ emission via the ${}^5\mathrm{H}$ ground state.

Figure 2

Experimental setup common for experiments 1 and 2 at the final focal plane F5 of the ACCULINNA-2 fragment separator. Detectors of ${}^8\mathrm{He}$ projectile positions (MWPC-1,2) and time-of-flight (ToF) are described in the text. There is no common scale along the beam axis in this plot. The telescope detectors of the reaction products ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are also shown in Figs. 3 and 4.

Figure 3

Charged particle detector telescopes used in experiment 1.

Figure 4

Charged particle detector telescopes used in experiment 2.

Figure 5

Identification of ${}^3\mathrm{H}$ by $\mathrm{\Delta }E\text{−}E$ method in the central telescope. The green dots show the double-coincidence ${}^3\mathrm{He}\text{−}{}^3\mathrm{H}$ events, assigned to the ${}^7\mathrm{H}$ spectrum in Fig. 10. The large red dots indicate ${}^7\mathrm{H}$ ground-state candidate events, see discussion of Sec. 3b.

Figure 6

Identification of ${}^3\mathrm{He}$ recoil nuclei by $\mathrm{\Delta }E\text{−}E$ method in four side telescopes. The green dots show the double-coincidence ${}^3\mathrm{He}\text{−}{}^3\mathrm{H}$ events, assigned to the ${}^7\mathrm{H}$ spectrum in Fig. 10. The large red dots indicate the ${}^7\mathrm{H}$ ground-state candidate events, see discussion of Sec. 3b.

Figure 7

Empty target correlated spectra $E_{\text{3H}}$ vs. $E_T$ (a) and ${\theta }_{\text{c.m.}}$ vs. $E_T$ (b) for ${}^7\mathrm{H}$ in experiment 2. Panel (c) shows all the data of experiment 2 in the plane ${\theta }_{\text{c.m.}}$ vs. $E_T$, see also Fig. 10. In all panels the red dots show the distribution for the events within the “kinematical triangle,” shown by gray color in panel (a); additional black dots show the rest of the data. The vertical gray dotted lines indicate assumed positions of the ${}^7\mathrm{H}$ resonant states, see Fig. 10. The vertical hatched area contains events either from “asymmetric” 5.5-MeV state or from the 5.5- to 7.5-MeV doublet. The line $E_{\text{3H}}<2/7E_T$ in panel (a) is discussed in Sec. 3b2.

Figure 8

The Monte Carlo simulations demonstrating the experiment 2 setup resolution for the ${}^2\mathrm{H}({}^8\mathrm{He},{}^3\mathrm{He}){}^7\mathrm{H}$ reaction. The simulations are performed for a set of fixed center-of-mass reaction angles ${\theta }_{\text{c.m.}}$ and the ${}^7\mathrm{H}$ decay energies $E_T$ indicated by green dots. The red dashed lines guide an eye along the contours defining the FWHM the for energy resolution, while the blue dotted lines do the same for the angular resolution.

Figure 9

Excitation spectrum of ${}^9\mathrm{Li}$ measured in the ${}^2\mathrm{H}({}^{10}\mathrm{Be},{}^3\mathrm{He}){}^9\mathrm{Li}$ reaction. The insert shows the part of the ${}^9\mathrm{Li}$ spectrum near the ground state. The red curve represents the Monte Carlo calculation of the ${}^9\mathrm{Li}$(g.s.) taking the parameters of the experimental setup.

Figure 10

(a) Correlation between the ${}^3\mathrm{H}$ energy in the ${}^7\mathrm{H}$ frame and the ${}^7\mathrm{H}$ decay energy derived from the data of experiment 2 (black circles). The large magenta circles show triple coincidence ${}^3\mathrm{He}\text{–}{}^3\mathrm{H}\text{–}n$ events. The shaded area corresponds to events matching a condition of maximal energy $E_{3\text{H}}<4/7E_T$ possible in the decay of ${}^7\mathrm{H}$. (b) The ${}^7\mathrm{H}$ MM spectrum projected from (a) by using a gate condition with cutoff $E_{3\text{H}}<4/7E_T$. The green-filled histogram shows the background inferred from the empty target data Fig. 7. (c) The ${}^7\mathrm{H}$ MM spectrum projected from (a) with the two selection gates, $E_{3\text{H}}<4/7E_T$ and ${\theta }_{\text{c.m.}}<{18}^{\circ }$. The magenta-filled histogram indicates the triple coincidence ${}^3\mathrm{He}\text{–}{}^3\mathrm{H}\text{–}n$ events. (d) Correlation between the ${}^3\mathrm{H}$ energy in the ${}^7\mathrm{H}$ frame and the decay energy of ${}^7\mathrm{H}$ from Ref. [36]. (e) The ${}^7\mathrm{H}$ MM-derived spectrum from Ref. [36]. (f) The ${}^7\mathrm{H}$ MM spectrum from Ref. [33]. The vertical gray dotted lines indicate the assumed positions of the ${}^7\mathrm{H}$ resonant states. The vertical hatched area contains events either from “asymmetric” 5.5 MeV state or from the 5.5- to 7.5-MeV doublet. The line $E_{\text{3H}}<2/7E_T$ in panel (a) is discussed in Sec. 3b2.

Figure 11

The missing mass spectrum obtained in experiment 2, in different representations. Two center-of-mass angular ranges are selected: The top row shows events selected by the gate ${\theta }_{\text{c.m.}}<{18}^{\circ }$, the bottom row shows spectra selected by the ${\theta }_{\text{c.m.}}>{18}^{\circ }$ condition. The binning factor and bin offset are shown for each column in the top row. The “phase-volume” curves $d\sigma /d{E}_{T}d\mathrm{\Omega }\approx E_T^5$ with experimental bias accounted by MC procedure are shown in the both rows (normalization is arbitrary).

Figure 12

The center-of-mass angular distributions for the ${}^2\mathrm{H}({}^8\mathrm{He},{}^3\mathrm{He}){}^7\mathrm{H}$ reaction in different ${}^7\mathrm{H}$ MM energy ranges. Efficiency corrected angular distributions are shown in the upper part of each panel. (a) The ${}^7\mathrm{H}$ ground state with $0<E_T<3.2\mathrm{MeV}$ and $E_{3\text{H}}<4/7E_T$, the hollow black and filled gray histograms shows the data of experiments 1 and 2, respectively. The dotted curves of corresponding color show the detection efficiency which is given on the right axis. The red solid curve shows the FRESCO calculation results with standard parameters, the blue dashed curve shows the result of FRESCO calculation assuming the extreme peripheral transfer (both curves have arbitrary scaling). (b) The first excited state (or doublet) with $3.2<E_T<8.5\mathrm{MeV}$. (c) The 11-MeV excited state with $10.5<E_T<12.5\mathrm{MeV}$. (d) The high-energy part of the spectrum with $E_T>12.5\mathrm{MeV}$.

Figure 13

The ${}^7\mathrm{H}$ center-of-mass $\varepsilon$ distribution of the ${}^3\mathrm{H}$ fragments emitted at the ${}^7\mathrm{H}\to {}^3\mathrm{H}+4n$ decay. The filled gray histogram is the distribution obtained in experiment 2 for the detected events with $E_T<3.2\mathrm{MeV}$. The gray solid and dotted curves show the theoretical (not corrected for experimental response) phase-volume distribution [see Eq. (3)] and the realistic distribution from Ref. [41], respectively. The curves labeled with the ${}^7\mathrm{H}$ ground-state decay energy $E_T$ show the MC-simulation results obtained for the phase-volume distribution of Eq. (3) at different decay energy values supposed for the ${}^7\mathrm{H}$ ground-state resonance.

Figure 14

The angular distributions of the ${}^3\mathrm{H}$ fragments in the laboratory frame relative to the ${}^7\mathrm{H}$ center-of-mass momentum vector. The ${}^7\mathrm{H}$ ground-state candidate events with $E_T<3.2\mathrm{MeV}$ are selected. (a) The experimental data and theoretical predictions with the experimental bias taken into account by the MC simulation. (b) The initial theoretical distributions based on phase-volume for different $E_T$ values. The curve designations are the same as in Fig. 13.

Figure 15

The energy profile of the ground and the first excited state(s) of ${}^7\mathrm{H}$. (a) Broad 5.5-MeV state case. The gray solid curve shows pure Lorentzian profile with $\mathrm{\Gamma }=1.5\mathrm{MeV}$. The black solid curve shows the realistic profile Eq. (4) with $\mathrm{\Gamma }=1.5\mathrm{MeV}$. The red dotted curve shows the realistic resonance profile with experimental resolution taken into account by the MC simulations. (b) Narrow 5.5-MeV states case. Black solid, blue dashed, and olive dash-double-dotted curves show the $5/2^{+}\text{–}3/2^{+}$ doublet with the resonance energies of 5.5 and 7.5 MeV, but with different widths of the $3/2^{+}$ resonance state. The red dotted and orange dash-dotted curves show the ground state plus doublet spectra with experimental resolution taken into account by the MC simulations. The ground-state width is assumed to be very small ($\mathrm{\Gamma }\lesssim 1$ keV) compared to energy resolution. The experimental ${}^7\mathrm{H}$ MM spectrum with gates $E_{3\text{H}}<4/7E_T$ and ${\theta }_{\text{c.m.}}<{18}^{\circ }$ is shown in both panels by gray histograms.