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recent observations of unevolved halo stars have confirmed the surprising linear relationship of the be and b abundances with [ fe / h ] ( @xcite , @xcite ) . this primary behaviour of be and b can not be understood on the basis of the standard model ( sm ) of libeb production in the interstellar medium ( ism ) from gcr spallation . this is because in the sm the libeb production rates are proportional to the global metallicity of the ism , so that a secondary behaviour with [ fe / h ] is expected . however , the sm assumes a _ gcr flux constant in time _ and equal to that currently oberved at the earth . there are many reasons to believe that the gcr flux was different in early epochs . in this contribution we solve the time - dependent propagation equation of crs in the galaxy in a simple and parametrized way to test whether the sm can be compatible with observations when the hypothesis of the cr flux constancy in time is relaxed . we consider a general time - dependent equation for the gcr propagation : @xmath0 where @xmath1 is the number density of gcr particles per energy interval as a function of energy per nucleon and time , @xmath2 is the loss time - scale including escape , @xmath3 , and inelastic nuclear interaction , @xmath4 . @xmath5 represents the ionization energy losses in the ism and finally , @xmath6 is the source spectrum of gcrs . we make the following assumptions :    \1 ) the energy and time dependences of @xmath7 , @xmath8 and @xmath9 are separable : @xmath10 2 ) we assume that gcrs are produced by supernovae ( sn ) so that @xmath11 , the sn rate , taken from a chemical evolution model which reproduces the current sn rates in the galaxy and the main characteristics of the solar neighbourhood . the source energy spectrum is : @xmath12^{1.5}}\ ] ] with @xmath13 mev . the constant @xmath14 is chosen in such a way that we can reproduce the observed current gcr flux at the earth . \3 ) @xmath2 can be split into two parts @xmath15 where @xmath16 represents the escape time - scale from the galaxy , and @xmath17 is the loss time - scale against inelastic nuclear interaction . the energy dependence of @xmath16 is taken from @xcite and that of @xmath17 from @xcite assuming a gas density of 1 @xmath18 . \4 ) the energy losses due to ionization in the ism have been considered according to @xcite . \5 ) the time - dependence of the ionization losses and of the inelastic nuclear interactions can be plausibly caused by temporal changes in the gas density . the time - dependence of the escape time - scale is more difficult to understand . here we treat it as a free parameter . for both we assume , for the sake of simplicity , exponential functions : @xmath19 where @xmath20 is the characteristic e - folding time of gas exhaustion in the galaxy and @xmath21 is the characteristic time - scale for variations of @xmath16 . we assume that @xmath2 was higher in the past , during the halo collapse ( t@xmath22 gyr ) . eq . ( 1 ) can be solved using the method of characteristics . the solution can be simplified considerably if @xmath23 yr . plausible values for @xmath20 and @xmath21 are longer than @xmath24 yr , so in that case the solution is @xmath25 where @xmath26 is the ionization energy loss time - scale calculated as : @xmath27 then , the rate of accumulation of libeb in the ism is calculated in the usual way ( see @xcite ) . we have considered the following cases :    * case 1 : * the energy dependence of the gcr source spectrum is given by eq . ( 3 ) with @xmath28 equal to the sn rate evolution . the remaining parameters are constant in time .    * case 2 : * case 1 plus @xmath29 from eq . ( 5 ) with @xmath30 gyr during the first 2 gyr of galactic evolution and @xmath31 afterwards ( i.e no time variation of @xmath32 ) . this means that the cr escape time - scale at @xmath33 was a factor @xmath34 higher than now . figures 1 and 2 show the calculated time - dependent gcr fluxes as well as the corresponding libeb evolution with [ fe / h ] . the results are :    * case 1 : * the flux is _ higher in the past _ and decreases slowly with time in the whole energy range . this higher flux implies a larger libeb production in the past than the sm model , although , this is still not enough to reproduce the observations .    * case 2 : * the flux in the past is _ also higher and the spectrum is flatter at energies e@xmath35 _ mev / n . in consequence the libeb production is even higher at early epochs than in _ case 1_. note that the predicted be evolution is nearly in agreement with the observations . on the other hand , the effect of considering the temporal evolution of the gas content in the galaxy is not very important for the libeb production . in this case the flux and spectrum are modified in a complex way depending on the value of @xmath20 and the interplay between @xmath36 and @xmath17 . our results show that variations of the gcr flux in time have to be considered to study the early production of libeb by spallation in the ism . a higher flux and a flatter cr spectrum in the past are able to improve the agreement between the predictions of the ( modified ) sm with observations . this is evident for be and b. for li , however , another important source of production is still required . a higher flux in the past can be achieved by taking into account the temporal evolution of the gcr sources , which is naturally explained by the temporal variation of the sn rate , or by assuming that the escape time - scale @xmath37 was higher in the past . the later assumption can improve the agreement between data and model considerably . however , it still requires a more solid theoretical justification ( @xcite ) . 99 duncan d.k . , primas f. , rebull l.m . , boesgaard a.m. , deliyannis c.p . , hobs l.m . , king j.r . , 1997 , 488 , 338 fields b. , olive k. , schramm d. 1994 , , 435 , 185 garca - lpez r. , lambert d.l , gustafsson b. , rebolo r. 1998 , ( in press ) garca - muoz m. , simpson j.a . , guzik t.g . , wefel j.p . , margolis s.h . , 1987 , s 64 , 269 longair m.s . 1992 , _ high energy astrophysics _ , cambridge university press , cambridge , p. 49 meneguzzi m. , audouze j. , reeves h. , 1971 , 15 , 337 prantzos n. , cass m. , vangioni - flam e. , 1993 , 403 , 630
it is well known that no time - independent galactic cosmic ray ( gcr ) flux model can account for the observed linear relationship of be and b abundances with metallicity . in this contribution 
 we solve the time - dependent cr propagation equation using simple analytic time dependences for the cr spectrum at the source , the galactic cr escape - length and gas density evolution . 
 the cr fluxes so obtained are used to study the early evolution of the libeb abundances in the galaxy .