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Register a new userProbing Nuclear forces beyond the drip-line using the mirror nuclei $^{16}$N and $^{16}$F
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I. Stefan
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Radioactive beams of $^{14}$O and $^{15}$O were used to populate the resonant states 1/2$^+$, 5/2$^+$ and $0^-,1^-,2^-$ in the unbound $^{15}$F and $^{16}$F nuclei respectively by means of proton elastic scattering reactions in inverse kinematics. Based on their large proton spectroscopic factor values, the resonant states in $^{16}$F can be viewed as a core of $^{14}$O plus a proton in the 2s$_{1/2}$ or 1d$_{5/2}$ shell and a neutron in 1p$_{1/2}$. Experimental energies were used to derive the strength of the 2s$_{1/2}$-1p$_{1/2}$ and 1d$_{5/2}$-1p$_{1/2}$ proton-neutron interactions. It is found that the former changes by 40% compared with the mirror nucleus $^{16}$N, and the second by 10%. This apparent symmetry breaking of the nuclear force between mirror nuclei finds explanation in the role of the large coupling to the continuum for the states built on an $ell=0$ proton configuration.
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The unbound proton-rich nuclei $^{16}$F and $^{15}$F are investigated experimentally and theoretically. Several experiments using the resonant elastic scattering method were performed at GANIL with radioactive beams to determine the properties of the low lying states of these nuclei. Strong asymmetry between $^{16}$F-$^{16}$N and $^{15}$F-$^{15}$C mirror nuclei is observed. The strength of the $nucleon-nucleon$ effective interaction involving the loosely bound proton in the $s_{1/2}$ orbit is significantly modified with respect to their mirror nuclei $^{16}$N and $^{15}$C. The reduction of the effective interaction is estimated by calculating the interaction energies with a schematic zero-range force. It is found that, after correcting for the effects due to changes in the radial distribution of the single-particle wave functions, the mirror symmetry of the $n-p$ interaction is preserved between $^{16}$F and $^{16}$N, while a difference of 63% is measured between the $p-p$ versus $n-n$ interactions in the second excited state of $^{15}$F and $^{15}$C nuclei. Several explanations are proposed.
A long-lived $J^{pi}=4_1^+$ isomer, $T_{1/2}=2.2(1)$ms, has been discovered at 643.4(1) keV in the weakly-bound $^{26}_{9}$F nucleus. It was populated at GANIL in the fragmentation of a $^{36}$S beam. It decays by an internal transition to the $J^{pi}=1_1^+$ ground state (82(14)%), by $beta$-decay to $^{26}$Ne, or beta-delayed neutron emission to $^{25}$Ne. From the beta-decay studies of the $J^{pi}=1_1^+$ and $J^{pi}=4_1^+$ states, new excited states have been discovered in $^{25,26}$Ne. Gathering the measured binding energies of the $J^{pi}=1_1^+-4_1^+$ multiplet in $^{26}_{9}$F, we find that the proton-neutron $pi 0d_{5/2} u 0d_{3/2}$ effective force used in shell-model calculations should be reduced to properly account for the weak binding of $^{26}_{9}$F. Microscopic coupled cluster theory calculations using interactions derived from chiral effective field theory are in very good agreement with the energy of the low-lying $1_1^+,2_1^+,4_1^+$ states in $^{26}$F. Including three-body forces and coupling to the continuum effects improve the agreement between experiment and theory as compared to the use of two-body forces only.
The parity-transfer $({}^{16}{rm O},{}^{16}{rm F}(0^-,{rm g.s.}))$ reaction is presented as a new probe for investigating isovector $0^-$ states in nuclei. The properties of $0^-$ states provide a stringent test of the threshold density for pion condensation in nuclear matter. Utilizing a $0^+ rightarrow 0^-$ transition in the projectile, the parity-transfer reaction transfers an internal parity to a target nucleus, resulting in a unique sensitivity to unnatural-parity states. Consequently, the selectivity for $0^-$ states is higher than in other reactions employed to date. The probe was applied to a study of the $0^-$ states in ${}^{12}{rm B}$ via the ${}^{12}{rm C}({}^{16}{rm O},{}^{16}{rm F}(0^-,{rm g.s.}))$ reaction at $247~{rm MeV/u}$. The excitation energy spectra were deduced by detecting the ${}^{15}{rm O}+p$ pair produced in the decay of the ${}^{16}{rm F}$ ejectile. A known $0^-$ state at $E_x = 9.3~{rm MeV}$ was observed with an unprecedentedly high signal-to-noise ratio. The data also revealed new candidates of $0^-$ states at $E_x=6.6 pm 0.4$ and $14.8 pm 0.3~{rm MeV}$. The results demonstrate the high efficiency of $0^-$ state detection by the parity-transfer reaction.
First on-line mass measurements were performed at the SHIPTRAP Penning trap mass spectrometer. The masses of 18 neutron-deficient isotopes in the terbium-to-thulium region produced in fusion-evaporation reactions were determined with relative uncertainties of about $7cdot 10^{-8}$, nine of them for the first time. Four nuclides ($^{144, 145}$Ho and $^{147, 148}$Tm) were found to be proton-unbound. The implication of the results on the location of the proton drip-line is discussed by analyzing the one-proton separation energies.
In a previous letter (Phys. Rev. Lett. 96, 072502 (2006)), the multi-channel algebraic scattering (MCAS) technique was used to calculate spectral properties for proton-unstable $^{15}$F and its mirror, $^{15}$C. MCAS achieved a close match to the then-new data for $p+^{14}$O elastic scattering and predicted several unusually narrow resonances at higher energies. Subsequently, such narrow resonance states were found. New cross section data has been published characterising the shape of the $J^pi =frac{1}{2}^-$ resonance. Herein we update that first MCAS analysis and its predictions. We also study the spectra of the set of mass-15 isobars, ${}^{15}$C, ${}^{15}$N, ${}^{15}$O, and ${}^{15}$F, using the MCAS method and seeking a consistent Hamiltonian for clusterisation with a neutron and a proton, separately, coupled to core nuclei ${}^{14}$C and ${}^{14}$O.
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