Under the assumption of isospin conservation in the strong interaction, mirror nuclei should have similar level schemes and excitation properties; however, when deviations from expected trends are observed in transition strengths of mirror nuclei, the opportunity may arise to learn about physics mechanisms to account for the isospin symmetry breaking phenomena.It is known that the isospin non-conserving force and Coulomb force can induce mirror energy differences. Nuclear shape changes among mirror nuclei may also change the balance of the transition strengths among mirror partners. The reduced transition strength $B$(E2) is proportional to the square of the proton matrix element $M_p$ and, therefore, measurements of the transition strength provide valuable data for comparison to shell-model calculations which utilize various effective interactions. Because the proton matrix element $M_p$ for a transition in one nucleus is equivalent to the neutron matrix element $M_n$ for the same transition in the mirror nucleus, measurements of mirror transitions provide a fuller picture of neutron and proton configurations for excited states, especially since the neutron matrix element is difficult to measure directly. Further, when measurements of mirror transitions are conducted within the same experiment, and the data are analyzed with the same methods, the resulting values of $M_n$ and $M_p$ may be compared more effectively due to reduction of systematic uncertainty associated with comparing results from different experiments or by different analysis methods. In this work, we have utilized the recoil-distance method (RDM) to measure the lifetimes of the $11/2^-$ states in mirror nuclei $^{39}$Ca and $^{39}$K by examining the analog $11/2^-\rightarrow 7/2^-$ transitions in both nuclei.The RDM lifetime measurements provide a model independent method of determining the $B$(E2) and, hence, the matrix elements $M_p$ and $M_n$ for the analog transitions. The measurements were performed utilizing the Coupled-Cyclotron Facility and A1900 fragment separator to produce a $^{42}$Sc secondary beam which was directed to the TRIPLEX device where reactions on a $^{9}$Be target produced $^{39}$Ca and $^{39}$K in excited states. The excited nuclei were identified in the S800 spectrograph and gamma rays were collected with the GRETINA array. The analysis methods employed for the lifetime measurement of the $11/2^-$ state in $^{39}$Ca were validated by comparing the $^{39}$K results to adopted values. Additionally, the data provide an improved lifetime measurement of the $9/2^-$ state in $^{39}$Ca. From the lifetime measurements, the reduced transition strengths $B$(E2) are determined for the $11/2^-\rightarrow 7/2^-$ mirror transitions. Using the matrix element decomposition, the $M_p$ and $M_n$ are determined and the results are compared to shell-model calculations which utilize three effective interactions common to this region of the nuclear chart. The comparison of the matrix elements to shell-model calculations suggests an enhanced transition strength in $^{39}$Ca, suggesting both proton and neutron contributions to core excitations across the $Z=N=20$ shell gaps.
Read
