One-proton and one-neutron knockout reactions from $N = Z = 28$ $^{56}$Ni to the $A = 55$ mirror pair $^{55}$Co and $^{55}$Ni

TL;DR

This study investigates the nuclear structure and mirror symmetry in $^{55}$Co and $^{55}$Ni through knockout reactions from $^{56}$Ni, revealing asymmetries in cross sections and decay patterns that challenge current models.

Contribution

It provides new experimental data on excited states and decay properties in mirror nuclei, highlighting asymmetries that test and challenge existing nuclear structure theories.

Findings

Identified mirror asymmetry in partial cross sections to low-lying states.

Observed significant differences in $E1$ decay patterns between mirror nuclei.

Revealed that current shell-model descriptions cannot fully explain the asymmetries.

Abstract

We present a high-resolution in-beam $\gamma$-ray spectroscopy study of excited states in the mirror nuclei $^{55}$Co and $^{55}$Ni following one-nucleon knockout from a projectile beam of $^{56}$Ni. The newly determined partial cross sections and the $\gamma$-decay properties of excited states provide a test of state-of-the-art nuclear structure models and probe mirror symmetry in unique ways. A mirror asymmetry for the partial cross sections leading to the two lowest $3/2^-$ states in the $A = 55$ mirror pair was identified as well as a significant difference in the $E1$ decays from the $1/2^+_1$ state to the same two $3/2^-$ states. The mirror asymmetry in the partial cross sections cannot be reconciled with the present shell-model picture or small mixing introduced in a two-state model. The observed mirror asymmetry in the $E1$ decay pattern, however, points at stronger mixing between the two lowest $3/2^-$ states in $^{55}$Co than in its mirror $^{55}$Ni.

Equations

$$|3/2_1^{-}⟩$$

$$|3/2_2^{-}⟩$$

Full text

We report on a study that uses mirrored one-neutron and one-proton knockout reactions from 56Ni to the mirror nuclei 55Ni and 55Co, respectively. Similar types of mirrored reactions have been employed before to extract MED in more distant mirror pairs such as (52Ni,52Cr) Davies et al. (2013), (53Ni,53Mn) Milne et al. (2016) and (70Se,70Kr) Wimmer et al. (2018), however, starting from projectiles that are mirrors themselves rather than from a self-conjugate nucleus. Brown et al. Brown et al. (2009) used the $\gamma$-ray spectra of 53Ni and 53Mn from the three-neutron and three-proton removal on 56Ni projectiles to match analog states but such reactions cannot be described within a direct reaction formalism.

The doubly-magic nucleus 56Ni and the $T=1/2$ ($T_{z}=\pm 1/2$) (55Co,55Ni) mirror pair are of particular interest as they are coming within reach of ab-initio-type calculations  Hagen et al. (2016); Hergert (2017) that compute nuclei based on forces from chiral effective field theory. 56Ni has also been a target for early large-scale configuration-interaction shell-model calculations in the full $pf$ model space Horoi et al. (2006), pioneering coupled-cluster calculations Horoi et al. (2007); Gour et al. (2008), and self-consistent Green’s function theory Barbieri (2009); Barbieri and Hjorth-Jensen (2009). Although nominally doubly-magic, 56Ni behaves as a soft core in shell-model calculations performed in the full $pf$ model space. Using the effective isospin-conserving GXPF1A interaction, the closed-shell $(1f_{7/2})^{16}$ configuration comprises only about 68 $\%$ of the ground-state wavefunction Honma et al. (2004). These calculations successfully account for the observed quadrupole collectivity Yurkewicz et al. (2004a) and the ground-state magnetic moments of the odd-$A$ neighbors with one nucleon added or removed Callaghan et al. (1973); Ohtsubo et al. (1996); Berryman et al. (2009); Cocolios et al. (2009).

In terms of single-particle properties, a number of experiments ENSDF ; Shoup et al. (1972); Fortier et al. (1977); Erlandsson and Lyttkens (1977); Zhou et al. (1996); Yurkewicz et al. (2006); Jiang et al. (2009); Lee et al. (2009); Schiffer et al. (2013); Sanetullaev et al. (2014) and theoretical studies Trache et al. (1996); Honma et al. (2004); Horoi et al. (2006, 2007); Barbieri (2009); Barbieri and Hjorth-Jensen (2009); Litvinova and Afanasjev (2011) have been performed to identify the fragments of the single-particle levels relative to the $N=Z=28$ core and have also suggested the existence of $(2^{+}_{1}({}^{56,58}\mathrm{Ni})\otimes 1f_{7/2}^{-1})$ core-coupled excitations with $J^{\pi}=3/2^{-},...,11/2^{-}$ in the vicinity of 56Ni Burton and McIntyre (1971); Brookes and Robertson (1987); Yurkewicz et al. (2004b). Only recently, an inverse-kinematics one-neutron transfer experiment ${}^{1}\mathrm{H}({}^{56}\mathrm{Ni},d){}^{55}\mathrm{Ni}$ populated for the first time single-hole-like states directly from the 56Ni ground state Sanetullaev et al. (2014), however, without detecting subsequent $\gamma$-ray emission. An excited $3/2^{-}$ and $1/2^{+}$ state were observed.

Relevant for this work, strong isospin mixing between the $T=3/2$, $J^{\pi}=3/2^{-}$ IAS of 55Cu and a very close-lying $T=1/2,J^{\pi}=3/2^{-}$ state was observed in a $\beta$-decay experiment leading to 55Ni Tripathi et al. (2013). Very similar observations had been made in the 1970s for the IAS of 55Fe in the mirror nucleus 55Co Shoup et al. (1972); Martin et al. (1976); Fortier et al. (1977). The recent $\beta$-decay data on 55Ni hint at slightly stronger isospin mixing in 55Co Tripathi et al. (2013) as compared to the earlier work mentioned above. The degree of isospin mixing between $T=0$ and $T=1$ components in the ground state of 56Ni has been controversially discussed. Some evidence comes from the detection of $\beta$-delayed protons after the $\beta^{+}$ decay of 57Zn ($T=3/2$), where both the $0^{+}_{1}$ and $2^{+}_{1}$ state in 56Ni ($T=0$) were strongly populated Jokinen et al. (2002).

Here, we investigate the single-particle structure of self-conjugate 56Ni and the mirrors 55Ni (55Co) using the $\gamma$-ray-tagged mirrored one-neutron (one-proton) knockout reactions. Mirror asymmetries in partial cross sections and $\gamma$-decay patterns will be discussed.

The experiment was performed at the Coupled Cyclotron Facility of the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University Gade and Sherrill (2016). The secondary beam of 56Ni was selected in flight with the A1900 fragment separator Morrissey et al. (2003) using a 300 mg/cm2 Al degrader after production from a 160 MeV/u 58Ni primary beam in projectile fragmentation on a thick 610 mg/cm2 9Be target. The 56Ni secondary beam was unambigiously distinguished from the 55Co (27 $\%$) and 54Fe (1 $\%$) contaminants via the time-of-flight difference measured between two plastic scintillators located at the exit of the A1900 and the object position of the S800 analysis beam line. A 188 mg/cm2 9Be reaction target was surrounded by the SeGA array consisting of 16 32-fold segmented High-Purity Germanium detectors Mueller et al. (2001). The detectors were arranged in two rings with central angles of 37*∘* (7 detectors) and 90*∘* (9 detectors) relative to the beam axis. The segmentation of the detectors enables an event-by-event Doppler reconstruction of the $\gamma$ rays emitted by the projectile-like reaction residues in flight ($v/c\approx 0.4$). The angle of the $\gamma$-ray emission needed for this reconstruction is determined from the segment position that registered the highest energy deposition. All projectile-like reaction residues entering the S800 focal plane were identified event-by-event from their energy loss and time of flight Bazin et al. (2003). The Doppler-corrected in-beam $\gamma$-ray singles spectra in coincidence with event-by-event identified knockout residues are shown in Fig. 1. Only a change in magnetic rigidity of the S800 spectrograph was required to switch from one knockout setting to the other.

Inclusive cross sections of $38.0\pm 0.2\,(\mathrm{stat.})\pm 3.0\,(\mathrm{sys.})$ mb for the one-neutron knockout from 56Ni to all bound states of 55Ni and of $126\pm 2\,(\mathrm{stat.})\pm 17\,(\mathrm{sys.})$ mb for the one-proton knockout to all bound final states of 55Co were determined. In both cases, the inclusive cross section was deduced from the yield of the detected knockout residues relative to the number of incoming 56Ni projectiles and the number density of the 9Be reaction target. Statistical and systematic uncertainties are quoted separately. The latter include the stability of the secondary beam composition, the choice of software gates, and corrections for acceptance losses in the tails of the residue parallel momentum distributions due to the blocking of the unreacted beam in the focal plane. The parallel momentum distribution of the knockout residues was reconstructed on an event-by-event basis using the two position-sensitive cathode readout drift counters of the S800 focal-plane detection system Bazin et al. (2003) in conjunction with trajectory reconstruction through the spectrograph.

To calculate the $\gamma$-ray yields needed to determine the partial cross sections to individual final states, GEANT4 simulations were performed with the UCSeGA simulation package ucs . The results of those simulations, assuming a smooth double-exponential background, are shown in Fig. 1 together with the measured $\gamma$-ray spectra. Possible sources of the in-beam background were discussed in, e.g., Stroberg et al. (2014); Podolyák et al. (2003); Weisshaar et al. (2008). Using $\gamma\gamma$ coincidences, feeders were identified and the placement of previously known $\gamma$-ray transitions in the level scheme ENSDF ; Tripathi et al. (2013) confirmed. The level schemes are displayed in Fig. 2.

Partial cross sections to individual final excited states in 55Ni and 55Co, feeding-corrected where possible, are presented in Figs. 3 (a), (b) along with the corresponding predictions of calculations, (c), (d), combining shell-model spectroscopic factors with eikonal reaction theory Tostevin (2001) following the approach outlined in Gade et al. (2008); Tostevin and Gade (2014). As input for the cross-section calculations, the valence-nucleon radial wavefunctions were calculated in a Woods-Saxon-plus-spin-orbit potential, the geometry of which is constrained by Hartree-Fock calculations using the SkX Skyrme interaction Alex Brown (1998). Shell-model calculations in the full $pf$ shell using the GXPF1A-cd-$pn$ Hamiltonian were used to compute the spectroscopic factors $C^{2}S(J^{\pi})$ between the 56Ni ground state and final states with $J^{\pi}$ in 55Co and 55Ni, which enter the knockout cross sections. GXPF1A is the isospin conserving part as obtained in Honma et al. (2002, 2004, 2005). The charge-dependent (cd) Hamiltonian from Ormand and Brown (1989) was added. The isotensor part of this Hamiltonian does not change the wavefunctions for states with $T=1/2$. The total wavefunctions were calculated in a proton-neutron basis ($pn$). For these shell-model calculations, the computer code NuShellX was utilized Brown (2014). For further details on the calculation of the theoretical cross sections, see the supplemental material sup . In addition to the absolute values, partial cross sections $\sigma_{\mathrm{part.}}$ relative to the inclusive cross section $\sigma_{\mathrm{inc.}}$ are shown in Fig. 3. The ground-state partial cross sections obtained from subtraction are 29.1(7) mb (77(2) $\%$) in 55Ni and 80(5) mb (63(4) $\%$) in 55Co. Those values are upper limits only due to the possibility of missed, weak feeding transitions.

For the states observed in this work, the MED are shown for completeness in the lower panel of Fig. 2 in comparison to the shell-model predictions with the GXPF1A-cd-$pn$ Hamiltonian ($pf$ states only). The theoretical MED differ by 50-80 keV. The negative values of the MED relative to the $A=55$ ground states might be interpreted in terms of an increase of the mean nuclear radii of the excited states relative to that of the ground state due to the increased occupancy of the $2p_{3/2}$ orbital and the connected contribution to the MED through changes in the bulk Coulomb energy from the difference in $Z$ between the mirrors Zuker et al. (2002); Bentley et al. (2015). This corresponds to the influence of the monopole radial term on the MED Bentley et al. (2015). An MED of -100 keV corresponds to a 1.0 $\%$ increase in the radius. This effect of an increased $2p_{3/2}$ occupancy on the charge radius is similar to the isotope shift of 1.2 $\%$ observed between 56Fe and 54Fe Minamisono et al. (2016). The MED for the $1/2^{+}$ and $3/2^{+}$ states relative to the $7/2^{-}$ ground state also show that the addition of the relativistic spin-orbit correction of order +100 to +200 keV (see Table IV in Nolan and Schiffer (1969)) as well as the correction for the Coulomb energy stored in a single-proton orbital are required Zuker et al. (2002), which corresponds to the influence of the monopole single-particle term on the MED Bentley et al. (2015). In both nuclei, the $1/2^{+}$ and $3/2^{+}$ states are comparably strongly populated (see Figs. 3 (a) and (b)). These states are expected to have significant contributions to their wavefunction from the $sd$ orbitals below the $N=Z=28$ shell closure and have been previously discussed in Sanetullaev et al. (2014), where the $1/2^{+}$ state in 55Ni was also strongly populated. The $3/2^{+}_{1}$ state had not been unambiguously identified ENSDF ; Sanetullaev et al. (2014). The measured parallel momentum distributions, see Fig. 4 for 55Ni, support a $3/2^{+}$ assignment based on the clear observation of a nucleon knockout from an $l=2$ orbital.

It is interesting to note that the possible $\left(9/2^{-},11/2^{-}\right)$ doublet of the (2^{+}_{1}(\hbox{{}^{56}Ni})\otimes 1f_{7/2}^{-1}) multiplet is weakly populated in this work, 1.42(10) mb (3.7(3) $\%$) in 55Ni and 8.2(3) mb (6.5(2) $\%$) in 55Co, respectively. The population of these states cannot proceed by a one-step knockout process from the 56Ni ground state. The population of such complex configurations has been reported before, possible due to the knockout from the excited $2^{+}_{1}$ state of the projectile (see the discussion in Stroberg et al. (2014); Mutschler et al. (2016)). It has been speculated in previous studies that such indirect reaction mechanisms result in downshifts observed for some parallel-momentum distributions Stroberg et al. (2014); Mutschler et al. (2016). As is shown in Fig. 4, the distributions for those states are indeed shifted to lower momenta while the simpler configurations such as the main fragment of the $1d_{3/2}$ state line up as expected from the eikonal theory. The structure assignment is supported by the observation of $B(E2;\left(9/2^{-},11/2^{-}\right)\rightarrow 7/2^{-}_{1})$ values simlar to the $B(E2;2^{+}_{1}\rightarrow 0^{+}_{1})$ of 56Ni Yurkewicz et al. (2004b); ENSDF . The present shell-model calculations predict large spectroscopic factors between the $2^{+}_{1}$ state of 56Ni and the $(9/2^{-},11/2^{-})$ states in the $A=55$ nuclei of $C^{2}S=1.62$ and $1.12$, respectively. Theoretically, these core-coupled states are located at energies of about 2.8 MeV.

We note that a discussion of the reduction factor $R_{s}=\sigma_{\mathrm{exp.}}/\sigma_{\mathrm{th.}}$, reported for a large body of consistently analyzed knockout reactions Gade et al. (2008); Tostevin and Gade (2014), is not very instructive here as knockout from the $sd$ shell is observed, which is outside of the model space employed by the present shell-model calculations. Nevertheless, we can make a consistency argument. The theoretically expected inclusive cross sections, including the $1/2^{+}$ and $3/2^{+}$ states with spectroscopic factors from Ref. Sanetullaev et al. (2014), are 85 mb in 55Ni and 101 mb in 55Co. For 55Ni this gives a reduction factor of $R_{s}=0.45(4)$ ($\Delta S=10.5$ MeV), consistent with expectations from Gade et al. (2008); Tostevin and Gade (2014). For the slightly more deeply-bound 55Co ($S_{p}>$ 5 MeV), we expect that more bound $sd$-shell strength has to be included. Based on 57Co Reiner et al. (1987), the $2s_{1/2}$ strength may be fully exhausted and 75% of the $1d_{3/2}$ strength may be found below 5.2 MeV. Assuming in addition a spectroscopic factor of 1 for the bound $1d_{5/2}$ strength, and subtracting the cross section of the indirect contribution identified above, leads to a reduction factor of 0.93(13) consistent with Gade et al. (2008); Tostevin and Gade (2014).

Besides the slightly stronger relative population of the $5/2^{-}_{1}$, $7/2^{-}_{2}$, $(9/2^{-},11/2^{-})$, and $1/2^{-}_{2}$ states in 55Co, the fragmentation of the spectroscopic strengths between the two lowest-lying $3/2^{-}$ states is very different (see Fig. 3 (a) and (b)). One has to consider that this difference may be caused by unobserved feeding (55Co is slightly more bound than 55Ni and will consequently have more bound excited states). For instance, the unplaced 1352 keV transition, if feeding the 2566 keV level, would decrease its direct partial cross section by $\sim$ 33 $\%$. The $\gamma$-ray yields needed for resolved transitions over an energy range from 0.5 MeV to 3 MeV to obtain comparable cross sections for the $3/2^{-}$ states due to unaccounted feeding were estimated. If collected in a single or even two transitions, all of those feeders should have been identified in the $\gamma$-ray singles spectra. If this asymmetry was indeed caused by different feeding, the needed strength would have to be fragmented over multiple transitions which all have to be below the detection limit of the present measurement. It should be mentioned that the number of levels observed to feed the $3/2^{-}_{2}$ state in 55Co is larger than in 55Ni (compare Fig. 2). Still, after subtraction, its partial cross section is larger.

The observed asymmetry in the partial cross sections is theoretically not expected for the $3/2^{-}$ states (compare Fig. 3 (c) and (d)). Therefore, spectroscopic factors $C^{2}S$ for the one proton transfer from 54Fe (ground state) to 55Co ($J^{\pi}=3/2^{-}_{i}$) were also calculated and compared to the data from Table 1 of Fortier et al. (1977). To obtain agreement between the shell-model spectroscopic factors and the experimentally determined ratio of $C^{2}S(3/2^{-}_{1})/C^{2}S(3/2^{-}_{2})=1.54(22)$ in 55Co, derived as the average from several 54Fe to 55Co transfer reactions Fortier et al. (1977), mixing amplitudes of $\alpha=0.995^{+0.003}_{-0.004}$ ($\alpha^{2}=0.990^{+0.005}_{-0.010}$) and $\beta=-0.10^{+0.04}_{-0.03}$ ($\beta^{2}=0.010^{+0.010}_{-0.005}$) result in a model with two unperturbed $3/2^{-}_{j}$ ($j=I,II)$ states. The wavefunctions of the mixed states are then given by:

[TABLE]

Without introducing this 0.5 $\%$ to 2 $\%$ mixing, the ratio between the corresponding shell-model spectroscopic factors would have been 2.35 ($C^{2}S(3/2^{-}_{1})=1.22$, $C^{2}S(3/2^{-}_{2})=0.52$). Applying the same mixing to the one-proton knockout from the 56Ni ground state to 55Co leads to spectroscopic factors of $0.181^{+0.002}_{-0.003}$ for $3/2^{-}_{1}$ and $0.006^{+0.003}_{-0.002}$ for $3/2^{-}_{2}$ (0.186 and 0.001 without mixing), respectively, not explaining the asymmetry in the partial cross sections reported here. The emerging contradictory picture prevents conclusions on the role of isospin mixing based on the asymmetry in the partial cross sections, $\sigma(3/2^{-}_{i})$, and suggests that unobserved feeding in the present data may indeed be a contributor.

However, independent from the cross-section discussion, the $\gamma$-decay pattern of the $1/2^{+}$ state, which is the main feeder of the $3/2^{-}$ levels, is also significantly different in the two mirror nuclei. The phase-space corrected $R(E1)_{3/2^{-}_{2}/3/2^{-}_{1}}$ ratios are 2.69(14) and 3.9(3) in 55Co and 55Ni, respectively. To put this into perspective, these numbers mean that $\sim$ 18 $\%$ of the feeding-uncorrected $\gamma$-ray yield of the $3/2^{-}_{2}$ state in 55Co is due to the decay of the $1/2^{+}$ state while this contribution is $\sim$ 55 $\%$ in 55Ni ($\sim$ 50 $\%$ and $\sim$ 48$\%$ for the $3/2^{-}_{1}$). The adopted lifetime of $\tau=71^{+260}_{-4}$ fs ENSDF and the newly determined branching ratio in 55Co allowed to calculate the reduced $B\left(E1;1/2^{+}\rightarrow 3/2^{-}_{i}\right)$ transition strengths to be $17.2^{+1.2}_{-13.5}$ mW.u. to the $3/2^{-}_{1}$ and $46^{+4}_{-36}$ mW.u. to the $3/2^{-}_{2}$, respectively. For low-lying $E1$ transitions, such rates are, despite the large uncertainty of the lifetime, significantly enhanced. As mentioned in the introduction, a clear change of the $E1$-decay behavior of an excited state between mirror nuclei, as observed here, has been attributed to isospin-mixing effects in the $A=35$ Ekman et al. (2004) and $67$ Orlandi et al. (2009) mirror pairs.

With the mixing amplitudes determined from the 54Fe$-{}^{55}$Co transfer data, two solutions for the unpertubed matrix elements $\langle 3/2^{-}_{I,II}|T(E1)|1/2^{+}_{1}\rangle$ can be obtained. The uncertainty of the absolute $B(E1)$ strengths due to the lifetime uncertainty is neglected in the following discussion. It will affect both values in the same way and, thus, not change the ratio between them. In the first case, both matrix elements are positive and large leading to $B(E1;1/2^{+}_{1}\rightarrow 3/2^{-}_{I,II})$ values of $23(3)$ mW.u. for the first and $40(3)$ mW.u. for the second unperturbed $3/2^{-}$ state, respectively. In the second case, where one of the $E1$ matrix elements is negative, $B(E1)$ values of $12(3)$ mW.u. and $51(3)$ mW.u. are obtained. In both cases the first $E1$ matrix element is also comparably large. We note that an $E1$ transition between pure $(2s_{1/2})^{-1}(1f_{7/2})^{8}$ hole and $(1f_{7/2})^{6}(2p_{3/2})^{1}$ particle configurations for the $1/2^{+}$ and $3/2^{-}$, respectively, would be forbidden. Consequently, more complex configurations have to be present to explain the enhanced $E1$ rates. In fact, the relative partial cross sections of 6.1(3) $\%$ in 55Ni and 6.6(3) $\%$ in 55Co are almost identical for the $1/2^{+}$ state (compare Fig. 3), which suggests a similar structure of the $1/2^{+}$ state in the mirror pair and supports the hypothesis that the observed change in the $E1$ decay pattern probes the degree of mixing between the two $3/2^{-}$ states. The amount of isospin mixing needed to explain the $E1$ asymmetry for a low-lying $7/2^{-}$ level in the $A=35$ and a $9/2^{+}$ state in the $A=67$ mirror nuclei was estimated to be on the order of 1 $\%$ to 5 $\%$ Ekman et al. (2004); Pattabiraman et al. (2008); Orlandi et al. (2009); Bizzeti et al. (2012). In contrast to Refs. Ekman et al. (2004); Pattabiraman et al. (2008); Orlandi et al. (2009); Bizzeti et al. (2012), no mixing for the initial and final states but only between the two final states was assumed in the mixing scenario discussed here. Interestingly, the unperturbed $R(E1)_{3/2^{-}_{II}/3/2^{-}_{I}}$ ratio is $4.3^{+1.7}_{-1.1}$ in the second case, i.e. closer to the experimentally observed ratio for 55Ni. The smaller experimentally observed $R(E1)$ ratio in 55Co might, thus, point at stronger mixing between the unperturbed $3/2^{-}$ states than in its mirror 55Ni.

In conclusion, we have performed the first mirrored one-nucleon knockout reactions on the self-conjugate nucleus 56Ni leading to the mirror pair (55Ni,55Co). From in-beam $\gamma$-ray spectroscopy, partial cross sections were determined and the $\gamma$-decay properties were studied for a number of excited states in 55Ni and 55Co. Several states carrying single-particle strength were populated in the $A=55$ mirror pair. The fragments of the $2s_{1/2}$ and $1d_{3/2}$ hole-states carry significant cross sections in both nuclei, emphasizing the necessity to include $sd$ orbitals for the description of nuclei in this region. Small cross sections to a potential doublet of core-coupled states $(2^{+}_{1}({}^{56}\mathrm{Ni})\otimes 1f_{7/2}^{-1})$, $(9/2^{-},11/2^{-})$, were also observed, together with a telltale downshift in their parallel momentum distributions, indicative of an indirect reaction pathway. A pronounced cross section asymmetry for the two lowest-lying $3/2^{-}$ states as well as a clear change in the $E1$ decay pattern of the $1/2^{+}_{1}$ level feeding the $3/2^{-}$ states were discussed. The high degree of mixing, that would be needed to explain the cross-section asymmetry in a two-level approach, cannot be reconciled with a comparison of data on the transfer from 54Fe to 55Co to the corresponding shell-model calculations preventing conclusions on the role of isospin mixing. The change in the $E1$ decay pattern, however, hints at stronger mixing between the $3/2^{-}$ states in 55Co than in its mirror 55Ni and reveals an unexpected mirror asymmetry close to the nominally doubly-magic $N=Z$ nucleus 56Ni.