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experimental information on nuclei far from stability constitutes a challenging test for the applicability of nuclear models and serves as a guidance for improvement of the models . radioactive ion beam facility plays a vital role in gathering such information . in a recent experiment at the oak ridge hribf , padilla - rodal _ et al . _ measured @xmath6 in @xmath7ge @xcite , which provides a complete view of @xmath8 data extended to the neutron - rich region , reaching the major shell closure at @xmath9 . it was also demonstrated @xcite that the observed @xmath5 values in @xmath7ge can be reproduced by using a shell model with the model space @xmath10 for both protons and neutrons . hence this work showed that the structure change in the exotic mass region could be microscopically studied by means of large - scale shell model calculation , which has become available only recently . large - scale shell model calculations have been applied to the study of @xmath0 magicity in refs . @xcite . the work of padilla - rodal _ et al . _ has stimulated our interest in the long - standing problem of structure change along the ge isotopic chain , particularly in the vicinity of @xmath0 . the experimental @xmath8 data shown in fig . 4 of ref . @xcite suggest that @xmath11ni can be regarded as a quasi - doubly - closed - shell nucleus , but the nature of the @xmath0 subshell closure is gradually destroyed as the proton number outside the @xmath12 orbit increases . the variation of @xmath8 along the @xmath13 axis reminds us of the old problem , much discussed in the 1970 s and 1980 s , of the structure change from the @xmath14 to @xmath15 ge isotope . references were listed , for instance , in ref . @xcite published in 1987 . a notable irregularity at @xmath0 was observed in the @xmath16 and @xmath17 reaction cross sections @xcite , which is characterized by a drastic drop of the second @xmath2 excitation energy in @xmath18ge . this is an unusually low excited @xmath2 state , showing a similar character as that of typical doubly - closed - shell nuclei . at @xmath0 , the drop of @xmath19 appears in coincidence with a remarkable enhancement of @xmath8 . these experimental data suggest that the structure of @xmath18ge with @xmath0 is very different from that of @xmath11ni studied in refs . @xcite . the structure changes in ge isotopes were discussed in terms of pairing correlation and shape change ( or shape coexistence ) by using various collective models @xcite . the interacting boson model @xcite reproduced the observed energy levels and @xmath5 values for @xmath20ge . however , a satisfactory microscopic explanation has not been seen . most of the early studies in the literature limited their discussion on the configuration change within the @xmath21 shell . contributions from the @xmath1 orbit were very little mentioned . these early studies are insufficient according to the new knowledge on the @xmath0 magicity obtained in refs . @xcite , which has emphasized that nucleons in the @xmath1 orbit play a crucial role in determining the structure of the @xmath0 isotones . thus , as a necessary requirement , a microscopic study for the structure in ge isotopes should include the @xmath1 orbit . in the previous publications @xcite , we have demonstrated the feasibility of a shell model description for @xmath22ge ( including odd - mass isotopes ) , and for some other neighboring nuclei of the mass region . in these studies , large - scale shell model calculations ( up to dimension @xmath23 ) were performed in the model space @xmath10 , the same model space as that of ref . the aim of the present article is twofold : to fill the gap in the ge isotopic chain that the previous shell model calculations have neglected , and to look for possible structure reasons that may explain the unsolved puzzle in the middle of the chain around @xmath0 . the extended pairing plus quadrupole ( @xmath24 ) hamiltonian @xcite is employed in the present work . this hamiltonian has recently been proposed and tested through several shell model applications . it should be stressed that this isospin - invariant hamiltonian includes strong proton - neutron interactions in both @xmath25 and @xmath26 channel . the single - particle energies in our model are @xmath27=0.00 , @xmath28=0.77 , @xmath29=1.11 , and @xmath30=2.50 ( in mev ) . in the present work that deals with a long isotopic chain , we use the @xmath31-dependent interaction strengths : @xmath32 mev for the monopole pairing force , @xmath33 mev for the quadrupole - quadrupole ( @xmath34 ) force , and @xmath35 mev for the octupole - octupole ( @xmath36 ) force . these are the same parameters as those in ref . the hamiltonian contains also five monopole correction terms ( see ref . the effective charges are @xmath37 and @xmath38 .    , @xmath39 , and @xmath19 for the ge isotopes from @xmath40 to 50 . calculated @xmath8 with two sets of effective charge are shown for comparison.,width=264,height=264 ]    our results are presented in fig . [ fig1 ] , where calculated @xmath8 , @xmath39 , and @xmath19 for the ge isotopes from @xmath41ge ( @xmath40 ) to @xmath42ge ( @xmath9 ) are compared with data . the calculation reasonably reproduces @xmath8 and @xmath19 at both ends of the isotopic chain with @xmath13 = 34 , 36 and @xmath13 = 48 , 50 , but fails to describe those in between . especially , the calculation could not reproduce the increasing trend of @xmath8 over @xmath0 and the drop of @xmath19 around this neutron number . we can get an improved agreement with the @xmath8 data for @xmath43ge and @xmath44ge ( see fig . [ fig1 ] ) if we enlarge the effective charges to @xmath45 and @xmath46 ( @xmath46 is taken from ref . @xcite and @xmath45 is fixed so as to reproduce @xmath8 in @xmath42ge ) . however , the use of larger effective charges destroys the good agreement for @xmath41ge and @xmath11ge already obtained in ref . moreover , the rise in effective charges does not seem to have any positive effect on enhancing @xmath8 at @xmath0 . it is thus clear that the problem must stem from deeper structure reasons , which can not be resolved simply by a global fit through effective charges . the above results indicate an inadequacy either in the interaction employed in the calculation , or in the model space for @xmath47ge in question . at present , there is no available effective interaction better than the extended @xmath24 interaction for ge isotopes in the model space @xmath10 . we thus proceed our study with the extended @xmath24 interaction and look for any possible reasons for this discrepancy . the enhancement of @xmath8 in the @xmath0 isotones from @xmath11ni to @xmath44sr has been qualitatively explained by langanke _ _ @xcite using the shell model monte carlo ( smmc ) approach , where a @xmath24 hamiltonian ( with no monopole terms ) is used but their model space is larger , which includes also the @xmath4 shell . it must be noted that the smmc calculation gives only total @xmath5 strength to excited @xmath48 states and does not give the energy of the @xmath49 state . the smmc calculation predicted a large neutron occupation number in the @xmath1 orbit ( @xmath50 ) , in contrast to our small value ( @xmath51 ) obtained for @xmath18ge . this gives us a hint that inclusion of the @xmath52 orbits may significantly enhance the role of the @xmath1 orbit through the pairing and quadrupole correlations when the fermi level moves toward the @xmath4 shell . the deficiency in our calculation may be due to the insufficient model space for the nuclei where neutrons start to occupy the @xmath53 and @xmath1 orbits .    the @xmath1 occupancy of neutrons is investigated in @xmath11ni with the ordinary shell model @xcite , in which the @xmath1 orbit is excluded from the model space for protons . the value @xmath54 obtained in ref . @xcite is considerably different from the smmc result @xmath55 @xcite . in another recent work @xcite , we have investigated @xmath11ni in the neutron model space @xmath10 assuming a @xmath56ni core . the shell model for neutrons also gives the value @xmath54 , similar to that in ref . these shell model calculations show that the ground state of this nucleus remains a transitional character to a superfluid phase . it is thus interesting to investigate whether the delicate structure changes from the @xmath14 to @xmath15 ge isotopes are caused by strong pairing correlations . we continue our study within the @xmath57 space as this model space is at present the largest possible for a full shell model diagonalization . within this truncated space , contributions from the @xmath58 orbits must be expressed in terms of effective interaction . we have made testing calculations with different monopole corrections , which effectively change the neutron @xmath1 occupation . however , moderate modifications for the monopole corrections can not produce a significant structure change near @xmath59 . on the other hand , it is expected that the effects of the @xmath58 orbits tend to strengthen the pairing and quadrupole correlations . we therefore consider to enlarge the quadrupole matrix element @xmath60 to mimic any effect from the missing @xmath58 orbits . note that the quadrupole matrix elements between the @xmath61 and @xmath62 orbits are nonzero and those between the @xmath21 and @xmath63 shells are zero ( the @xmath64 orbit nearest to @xmath61 has the largest quadrupole matrix element with @xmath61 ) . based on the above considerations , we write the effective quadrupole matrix element for the @xmath1 orbit by multiplying a factor @xmath65 @xmath66 physically , an @xmath67 factor strengthens the @xmath34 force with respect to the @xmath1 orbit , which is consistent with the expectation that the ge isotopes become deformed at the beginning of the @xmath1 orbit and that a strong @xmath34 force contributes to lowering of the @xmath1 orbit . a stronger @xmath60 increases also the effective charges selectively for the @xmath1 nucleons . in our shell model treatment , we transform the @xmath34 force into multipole - pairing - type interactions in the particle - particle channel . thus effectively , a stronger @xmath34 force with respect to the @xmath1 orbit enhances also the pairing correlations , which allows more nucleons to jump to the @xmath1 orbit .    , @xmath39 , and @xmath19 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=264,height=241 ] , @xmath39 , and @xmath19 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=264,height=241 ] , @xmath39 , and @xmath19 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=264,height=241 ]    the effects from the @xmath58 orbits are considered to be isotope dependent and should become larger as the fermi level moves up . thus in our trial calculations , we assume an empirical expression for @xmath65 , @xmath68 . with these considerations , the calculations indeed achieve a great improvement in excitation energies @xmath39 and @xmath19 , especially for @xmath69ge . the calculated @xmath8 values remain good at the beginning of the chain ( @xmath13 = 34 and 36 , because the configurations are almost exhausted by the @xmath21 shell ) , and are enhanced at the end with @xmath13 = 46 @xmath70 50 . these improvements support the use of effective quadrupole matrix element @xmath71 . however , @xmath8 for @xmath72ge are again not enhanced . this indicates that the microscopic content in the wave - functions has not been improved . as a matter of fact , the neutron and proton occupation numbers @xmath73 and @xmath74 obtained for @xmath18ge ( @xmath0 ) by using @xmath71 can not bear a comparison with the large values @xmath75 and @xmath76 reported in ref . the large @xmath8 value in @xmath18ge corresponds to a large occupation of the @xmath1 orbit , which must be due to the pairing correlations in addition to the @xmath34 force . in fact , the unusually low energy of the second @xmath2 state in @xmath18ge implies a delicate balance between the pairing correlations and the energy gap @xmath77 . it has been pointed out by schiffer _ _ @xcite and utsuno _ et al . _ @xcite that the  effective energy " of the intruder states changes rapidly around a closed subshell in neutron - rich nuclei , and these changes were discussed in terms of the spin - orbit interaction or the spin - isospin dependence of nucleon - nucleon interaction . in our case , the change of the effective energy gap @xmath77 could be attributed to the pairing correlations in the @xmath4 shell . a good effective hamiltonian in a full shell model should be able to describe the balance microscopically . in the present work with the truncated model space , we try to understand the problem by simulating the underlying physics . namely , we adjust the energy gap @xmath78 and study any resultant change in @xmath8 and @xmath19 . we study variations of @xmath8 and @xmath19 in @xmath69ge as a function of single - particle separation energy between the @xmath1 and @xmath53 orbits . in the calculation , we use the enhancement factor @xmath79 for @xmath80ge , and a slightly larger one @xmath81 for @xmath82ge . interesting results are obtained as shown in fig . the circled areas represent the best choices in parameter that can describe the observed @xmath8 , and at the same time , give correct sequences of @xmath83 and @xmath49 in @xmath84ge . figure [ fig2 ] indicates clearly the necessity of a rapid lowering of the single - particle energy @xmath30 from the original value 2.5 mev in @xmath85ge , to @xmath86 2.0 mev in @xmath43ge , to @xmath86 1.75 mev in @xmath18ge , and to @xmath86 1.5 mev in @xmath82ge . thus the calculation demonstrates that the observed enhancement in @xmath8 and variation in @xmath19 correlate closely with the single - particle energy separation . data can not be understood unless the effective energy gap @xmath78 near @xmath0 is set to be small . on the other hand , the calculated @xmath8 in @xmath18ge and @xmath82ge can not reach the observed large values unless the enlarged matrix element @xmath71 is used . in particular , the correct sequence of the @xmath49 and @xmath83 states in @xmath82ge can not be obtained without narrowing the effective gap @xmath77 to a sensitive region in the parameter space , which implies an extremely delicate balance between the pairing correlations and the energy separation @xmath77 .    , @xmath39 , and @xmath19 in @xmath87ge as @xmath30 approaches @xmath29.,width=264,height=241 ]    although a meaningful parameter choice can be found for the isotopes up to @xmath82ge , it is difficult to go beyond them and find good parameters that can simultaneously reproduce @xmath8 and @xmath19 for @xmath87ge , as illustrated in fig . this indicates limitations in our renormalization approach within the truncated model space missing @xmath58 orbits above @xmath1 . as we shall see in sect . iv , a small energy separation @xmath88 causes nucleons to jump to the @xmath1 orbit easily , and with more nucleons in the @xmath1 orbit the use of @xmath71 enhances @xmath5 values in @xmath84ge . however , the situation seems to be different between @xmath84ge and @xmath87ge . in @xmath84ge , the @xmath1 orbit is occupied by at most four neutrons . in @xmath87ge , however , about half of the neutron @xmath1 orbit is occupied . with an additional neutron pair in the @xmath1 orbit , @xmath71 enhances @xmath5 exaggeratedly . in such a case , our renormalization approach fails to work properly . it would be necessary for the description of the @xmath89 isotopes to explicitly include upper orbits such as @xmath90 , as suggested in ref . below , we continue our discussion but focus the attention on the structure change in @xmath43ge , @xmath18ge , and @xmath82ge only .    , @xmath39 , and @xmath19 with experimental data.,width=264,height=264 ]    with the above adjustment in @xmath77 and the use of effective quadrupole matrix element @xmath71 , we are able to reproduce correctly all the observed variations in @xmath8 , @xmath19 , and @xmath39 for @xmath69ge , as summarized in fig . [ fig4 ] . here , the energy separation @xmath78 is not required to change for the @xmath41ge and @xmath11ge calculations if @xmath71 with @xmath91 is used . figure [ fig4 ] shows that the variation trend of @xmath92 energy is also correctly reproduced . of course , our simulated calculation does not provide a final answer to the problem , but is quite suggestive . it should be stressed that the set of circles in fig . [ fig2 ] is the sole selection in parameter that can describe the experimental data . the important information extracted from the above discussions is that in order to describe all the observed quantities in ge isotopes , it is necessary to have enough @xmath1 contributions in the wave - functions . next , let us study how the @xmath1 proton and neutron occupations correlate with the observations and how they vary in @xmath3ge . we calculate occupation numbers @xmath93 for protons and neutrons as functions of the energy separation @xmath78 , and focus our discussion on the results in the circled area that have reproduced data . figure [ fig5 ] shows that in @xmath43ge , a considerable number of neutrons occupy the @xmath1 orbit ( @xmath94 ) while protons are scarcely found in this orbit . for the ground state of @xmath18ge , the occupation numbers become @xmath95 and @xmath96 . these occupation numbers are consistent with those of ref . @xcite , though our value @xmath97 is larger . the result indicates a superfluid state for neutrons in @xmath18ge , in contrast to the narrow subshell closure in @xmath11ni @xcite . it is notable that in the circled area for @xmath18ge , the coupling between the @xmath98 and @xmath49 states becomes significant and a considerable number of protons occupy the @xmath1 orbit , which shows a qualitative difference from the structure in @xmath43ge . the structure in @xmath82ge again differs qualitatively from @xmath18ge . as @xmath30 approaches @xmath29 , the proton occupation numbers @xmath99 for @xmath98 and @xmath49 are reversed . for @xmath100 mev with which the calculated @xmath8 are comparable with data , more than four neutrons occupy the @xmath1 orbit and protons occupy this orbit also considerably , in sharp contrast to the situation in @xmath43ge .     and @xmath101 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=160,height=188 ]   and @xmath101 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=160,height=188 ]   and @xmath101 in @xmath3ge as @xmath30 approaches @xmath29.,title="fig:",width=160,height=188 ]    thus the structure differences appearing in our calculation for the two lowest @xmath2 states , @xmath98 and @xmath49 , may offer a new explanation for the old problem observed in @xmath16 and @xmath17 reactions . our simulated calculation predicts that the proton structure in the @xmath1 orbit is very different among the states in @xmath3ge . the proton @xmath1 occupation changes from a negligible amount in @xmath43ge to a considerable amount in @xmath102ge , and in addition , with a different distribution in the @xmath98 and @xmath49 states . obviously , these results can not be obtained without the presence of strong proton - neutron correlations in the model , which are important for nuclei where protons and neutrons occupy the same shell . the energy difference @xmath103 mev used in our calculation , which is adopted so as to well describe @xmath85ge @xcite and also consistent with the value used in ref . @xcite , is rather small . still , for the isotopes up to @xmath43ge , the proton occupation number @xmath99 remains small , in contrast to the strong configuration mixing within the @xmath21 shell including the @xmath53 orbit . in this sense , for protons when @xmath104 , there exists a gap between the @xmath105 shell and @xmath1 . however , as clearly seen from fig . [ fig5 ] , the proton occupation number @xmath99 , together with the neutron occupation number @xmath101 , increases suddenly in @xmath18ge and @xmath82ge . resonance " effect of @xmath99 and @xmath106 can be best attributed to strong proton - neutron correlations . similar effects are obtained in the smmc calculations for the @xmath0 isotones @xcite , where a larger energy difference @xmath107 ( or 1.97 ) mev is used but upper @xmath58 orbits above @xmath1 are included in the model space . a considerably large number of @xmath99 starts from @xmath18ge ( where @xmath108 is only equal to 32 and @xmath13 takes the magic number 40 ) . we may thus conclude that the proton @xmath1 occupancy must be caused by the proton - neutron correlations in the @xmath63 shell . our treatment with small @xmath78 and large @xmath60 is considered to mimic the effects , since the mechanism is not properly included in the model . it should be noted in this regard that our isospin - invariant hamiltonian treats dynamically the strong proton - neutron interactions . in conclusion , inspired by the recent experimental advances in @xmath5 measurement for neutron - rich ge isotopes , we have carried out a systematical shell model calculation for @xmath109ge in the model space @xmath10 . the calculations have shown that the strong enhancement of @xmath8 and the unusually low excitation of the second @xmath2 state near @xmath0 can be explained only with sufficient occupation of protons and neutrons in the @xmath1 orbit . the simulated calculations that mimic such effects have suggested a possible understanding of the structure change from @xmath43ge to @xmath82ge in terms of rapid increase in the number of @xmath1 protons and neutrons . this could be the source for the long - standing problem that has not yet been understood . the isotopic dependence of the @xmath1 proton occupation must have an origin of strong proton - neutron interactions .    in principle , it is a very difficult question whether all these effects can be expressed in an effective interaction . the calculations in ref . @xcite pointed out that the @xmath90 orbit above the @xmath1 makes a considerable contribution when @xmath110 in cr and fe isotopes apart from the proton magic number @xmath111 . the smmc calculations in the @xmath112 space @xcite also suggested an important role of the @xmath90 orbit in the enhancement of @xmath1 occupancies in those nuclei that have sufficient number of protons in the upper @xmath113 shell . according to the extended @xmath24 model , we can suggest that the pairing and quadrupole - quadrupole correlations in the major shell @xmath4 make it easier for protons and neutrons to be excited from the @xmath113 shell to the @xmath1 orbit . the present investigation with enlarged @xmath60 and decreased energy gap @xmath78 is along the line of this thought . the problem may be thoroughly explained if shell model calculations are performed in a two - major - shell - space including both @xmath113 and @xmath4 .
the long - standing problem of dramatic structure change near @xmath0 in ge isotopes is investigated by means of large - scale shell model calculation . 
 the analysis of simulated calculations suggests a possible understanding of the problem in terms of rapid increase in the @xmath1 proton and neutron occupation . 
 the observed variation in excitation of the second @xmath2 state in @xmath3ge appears to correlate closely with the @xmath1 occupations induced by strong proton - neutron interactions . 
 the enhancement of the @xmath1 occupancies is probably due to correlations in the @xmath4 shell . 
 ,    ,    ,    @xmath3ge , structure change , @xmath5 , second @xmath2 energy , shell model    27.50.+e , 23.20.lv , 21.10.re , 21.60.cs