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Register a new userBroken mirror symmetry in $^{36}$S and $^{36}$Ca
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Shape coexistence is an ubiquitous phenomenon in the neutron-rich nuclei belonging to (or sitting at the shores of) the $N=20$ Island of Inversion (IoI). Exact isospin symmetry predicts the same behaviour for their mirrors and the existence of a proton-rich IoI around $Z=20$, centred in the (surely unbound) nucleus $^{32}$Ca. In this article we show that in $^{36}$Ca and $^{36}$S, Coulomb effects break dramatically the mirror symmetry in the excitation energies, due to the different structures of the intruder and normal states. The Mirror Energy Difference (MED) of their 2$^+$ states is known to be very large at -246 keV. We reproduce this value and predict the first excited state in $^{36}$Ca to be a 0$^+$ at 2.7 MeV, 250 keV below the first 2$^+$. In its mirror $^{36}$S the 0$^+$ lies at 55 keV above the 2$^+$ measured at 3.291 MeV. Our calculations predict a huge MED of -720 keV, that we dub Colossal Mirror Energy Difference (CMED). A possible reaction mechanism to access the 0$^+_2$ in $^{36}$Ca will be discussed. In addition, we theoretically address the MEDs of the $A=34$ $T=3$ and $A=32$ $T=4$ mirrors.
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A recent sensitivity study has shown that the $^{35}$K$(p,gamma)^{36}$Ca reaction is one of the ten $(p,gamma)$ reaction rates that could significantly impact the shape of the calculated X-ray burst light curve. In this work, we propose to reinvestigate the $^{35}$K$(p,gamma)^{36}$Ca reaction rate, as well as related uncertainties, by determining the energies and decay branching ratios of $^{36}$Ca levels, within the Gamow window, in the 0.5 to 2 GK X-ray burst temperature range. These properties were studied using the one neutron pick-up transfer reaction $^{37}$Ca$(p,d)^{36}$Ca in inverse kinematics using a radioactive beam of $^{37}$Ca at 48 MeV nucleon$^{-1}$. The experiment performed at GANIL, used the liquid Hydrogen target CRYPTA, the MUST2 detector array for the detection of the light charged particles and a zero degree detection system for the outgoing heavy ions. The atomic mass of $^{36}$Ca is confirmed and new resonances have been proposed together with their proton decay branching ratios. This spectroscopic information, used in combination with recent theoretical predictions for the $gamma$-width, were used to calculate the $^{35}$K$(p,gamma)^{36}$Ca reaction rate. The recommended rate of the present work was obtain within a uncertainty factor of 2 at 1 sigma. This is consistent, with the previous estimate in the X-ray burst temperature range. A large increase of the reaction rate was found at higher temperatures due to two newly discovered resonances. The $^{35}$K$(p,gamma)^{36}$Ca thermonuclear reaction rate is now well constrained by the present work in a broad range of temperatures. Our results show that the $^{35}$K$(p,gamma)^{36}$Ca reaction does not affect the shape of the X-ray burst light curve, and that it can be removed from the list of the few influential proton radiative captures reactions having a strong impact on the light curve.
Isobaric quintets provide the best test of the isobaric multiplet mass equation (IMME) and can uniquely identify higher order corrections suggestive of isospin symmetry breaking effects in the nuclear Hamiltonian. The Generalized IMME (GIMME) is a novel microscopic interaction theory that predicts an extension to the quadratic form of the IMME. Only the $A=20, 32$ $T=2$ quintets have the exotic $T_z = -2$ member ground state mass determined to high-precision by Penning trap mass spectrometry. In this work, we establish $A=36$ as the third high-precision $T=2$ isobaric quintet with the $T_z = -2$ member ground state mass measured by Penning trap mass spectrometry and provide the first test of the predictive power of the GIMME. A radioactive beam of neutron-deficient $^{36}$Ca was produced by projectile fragmentation at the National Superconducting Cyclotron Laboratory. The beam was thermalized and the mass of $^{36}$Ca$^+$ and $^{36}$Ca$^{2+}$ measured by the Time of Flight - Ion Cyclotron Resonance method in the LEBIT 9.4 T Penning trap. We measure the mass excess of $^{36}$Ca to be ME$ = -6483.6(56)$ keV, an improvement in precision by a factor of 6 over the literature value. The new datum is considered together with evaluated nuclear data on the $A=36$, $T=2$ quintet. We find agreement with the quadratic form of the IMME given by isospin symmetry, but only coarse qualitative agreement with predictions of the GIMME. A total of three isobaric quintets have their most exotic members measured by Penning trap mass spectrometry. The GIMME predictions in the $T = 2$ quintet appear to break down for $A = 32$ and greater.
Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in the isotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values were reported by using the major fragments of the states. An important reduction of the $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to a strong modification of the spin--orbit potential in the central region of the nucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings in the $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ several Skyrme and Gogny interactions, to reliably isolate pure spin--orbit and tensor--induced contributions, within the mean--field approximation. We use interactions (i) without the tensor force; (ii) with the tensor force and with tensor parameters adjusted on top of existing parametrizations; (iii) with the tensor force and with tensor and spin--orbit parameters adjusted simultaneously on top of existing parametrizations. We predict in cases (ii) and (iii) a non negligible reduction of both $p$ and $f$ splittings, associated to neutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittings are further decreased for the three types of interactions, going from $^{36}$S to $^{34}$Si. This reduction is produced by the spin--orbit force and is not affected by tensor--induced contributions. For both reductions, from $^{40}$Ca to $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that the modification is more pronounced for $p$ than for $f$ splittings. The measurement of the centroids for neutron $2p$ and $1f$ states in the nuclei $^{36}$S and $^{34}$Si would be interesting to validate this prediction experimentally. We show the importance of using interactions of type (iii), because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which are in agreement with the corresponding experimental values.
The difference between observed cross sections of the evaporation residues (ER) of the $^{34}$S+$^{208}$Pb and $^{36}$S+$^{206}$Pb reactions formed in the 2n and 3n channels has been explained by two reasons related with the entrance channel characteristics of these reactions. The first reason is that the capture cross section of the latter reaction is larger than the one of the $^{34}$S+$^{208}$Pb reaction since the nucleus-nucleus potential is more attractive in the $^{36}$S+$^{206}$Pb reaction due to two more neutrons in isotope $^{36}$S. The second reason is the difference in the heights of the intrinsic fusion barrier $B^*_{rm fus}$ appearing on the fusion trajectory by nucleon transfer between nuclei of the DNS formed after the capture. The value of $B^*_{rm fus}$ calculated for the $^{34}$S+$^{208}$Pb reaction is higher than the one obtained for the $^{36}$S+$^{206}$Pb reaction. This fact has been caused by the difference between the $N/Z$-ratios in the light fragments of the DNS formed during the capture in these reactions. The $N/Z$-ratio has been found by solution of the transport master equations for the proton and neutron distributions between fragments of the DNS formed at capture with the different initial neutron numbers $N=18$ and $N=20$ for the reactions with the $^{34}$S and $^{36}$S, respectively.
The evolution of nuclear magic numbers at extremes of isospin is a topic at the forefront of contemporary nuclear physics. $N=50$ is a prime example, with increasing experimental data coming to light on potentially doubly-magic $^{100}$Sn and $^{78}$Ni at the proton-rich and proton-deficient extremes, respectively. Experimental discrepancies exist in the data for less exotic systems. In $^{86}$Kr the $B(E2;2^+_1rightarrow0^+_1)$ value - a key indicator of shell evolution - has been experimentally determined by two different methodologies, with the results deviating by $3sigma$. Here, we report on a new high-precision measurement of this value, as well as the first measured lifetimes and hence transition strengths for the $2^+_2$ and $3^-_{(2)}$ states in the nucleus. The Doppler-shift attenuation method was implemented using the TIGRESS gamma-ray spectrometer and TIGRESS integrated plunger (TIP) device. High-statistics Monte-Carlo simulations were utilized to extract lifetimes in accordance with state-of-the-art methodologies. Lifetimes of $tau(2^+_1)=336pm4text{(stat.)}pm20text{(sys.)}$ fs, $tau(2^+_2)=263pm9text{(stat.)}pm19text{(sys.)}$ fs and $tau(3^-_{(2)})=73pm6text{(stat.)}pm32text{(sys.)}$ fs were extracted. This yields a transition strength for the first-excited state of $B(E2;2^+_1rightarrow0^+)=259pm3text{(stat.)}pm16text{(sys.)}$ e$^2$fm$^4$. The measured lifetime disagrees with the previous Doppler-shift attenuation method measurement by more than $3sigma$, while agreeing well with a previous value extracted from Coulomb excitation. The newly extracted $B(E2;2^+_1rightarrow0^+_1)$ value indicates a more sudden reduction in collectivity in the $N=50$ isotones approaching $Z=40$.
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