ࡱ> n7 MbjbjUU 7|7|ClFFFZ8@\Z.|!($"$"$"###-------$H/ h1-QF##"###-'$"$"L.'''#lR$"F$"-'#-''-$"F-$"p Ψ,Ze%--,b.0.- 2I' 2-'ZZ Variational study of fermionic helium dimer and trimer in two dimensions It is dedicated to Academician Krunoslav Ljolje in honor of his 70th birthday L.Vranjea and S. Kili Faculty of Natural Science, University of Split, 21000 Split, Croatia March 15, 2000 Abstact In variational calculation we obtain binding energy of helium 3 dimer in two dimensions. The existence of one bound state, with binding energy -0.014 mK, has been definitively found. Also, the existence of a binding state of helium 3 trimer having spin-1/2 with the energy below -0.0057 mK is indicated. This reopens the question of the existence of the gas phase of many helium 3 atoms on a surface of superfluid helium 4. PACS: 36.90. +f, 31.20. Di 1 Introduction About thirty years ago it was demonstrated [1] that in dilute bulk 3He - 4He solution atoms of 3He prefer to float on the surface of the 4He rather than to be dissolved in the bulk. All atoms in the solution are pulled down by gravity. A 3He atom is less massive than a 4He atom and therefore its zero point motion energy is greater than that of 4He (for a factor 1.3 approximately). Due to this motion it tends to have no 4He nearby. This tendency leads it to sit on the surface of the 4He, where it has empty space above. Thus a 3He atom at low temperatures (below 0.1 K), on the surface of bulk liquid 4He behaves as a spin-1/2 Fermi particle in two dimensions. In our recent papers [2, 3, 4] we have considered binding of helium diatomic molecules in confined and unconfined geometries. It has been shown that in infinite space helium fermionic dimer exists only in two dimensions. In confined geometry two helium atoms were studied in 2 and 3 dimensions. Motion of atoms has been confined by spherically external holding potentials [2]. Using similar procedure diatomic helium molecules have been studied in external holding potential that depends on one coordinate as well [4]. All considered systems might be thought as models for the interactions between helium atoms in specific real physical environment. For example, in solid matrices, where helium dimers form the condensation seed for helium clusters, in nanotubes, with a diameter between 10 and 100 , and in "condensation" on a solid or liquid substrate. We are not convinced that the atoms of 3He form a gas on a surface. This doubt is based on the fact that there is one bound state of two 3He atoms in 2 D space with binding energy of about -0.02mK [2]. This result was achieved after numerical solving Schrdinger equation. Of course a variational calculation is desired as well. A successful variational calculation showing binding of helium 3 dimer in 2 D, has not been done so far. The first goal of this paper is to derive a trial radial wave function and perform variational calculation in finding binding energy of fermionic helium 3 dimer in 2 D and mean value of the internuclear distance (Sec. 2 and 3.). The second goal is to examine the possibility of the existence of helium 3 trimer with spin-1/2 (Sec. 4). In Sec. 5 a discussion of our results is presented. 2 A derivation of trial wave function Very good trial wave functions describing ground state of helium 4 dimer and molecule consisting of one atom of helium 4 and one atom of helium 3, were obtained and used in ref. [2]. They describe short-range correlation between two atoms, like in Jastrow wave function for liquid helium state. Long-range correlations are described by decreasing exponential function. Comparing our results with the numerical solution of Schredinger eq. we found that the best form was a product of the functions, which describe short and long range correlations divided by the square root of the distance:  EMBED Equation.3 , (1) where a, ( and s are variational parameters. Our experience showed that this function, although very good for helium 4 dimer and 4He-3He molecule, was not enough good to give bound state of the fermionic helium dimer. This dimer is very large (the largest molecule we know) and behaviour of the wave function in between short and long range is very important. Using Gnuplot graphics and data from numerical solution of Schrdinger equation we were able to construct the following trial wave function.  EMBED Equation.3 , (2) where  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3 ,  EMBED Equation.3  and r1=1 , r2=2.97 , r3=34.57 , r4=165.1 , r5=228.5 , r6=2000 . It has 17 parameters a1, a2, a3, b1, b2, b3, c1, c2, c3, d1, d2, d3, e1, e2, e3, g1, s and 8 of them are independent. Namely, using the continuity of the wave function and first derivative in points r2, to r6, one finds the following nine equations among the parameters; there would be ten, but our wave function has its maximum at point  EMBED Equation.3  and the equation which demands continuity of the first derivative disappears (with the constraint that EMBED Equation.3 ):  EMBED Equation.3 , (3)  EMBED Equation.3 , (4)  EMBED Equation.3 , (5)  EMBED Equation.3 , (6)  EMBED Equation.3 , (7)  EMBED Equation.3 , (8)  EMBED Equation.3 , (9)  EMBED Equation.3 , (10)  EMBED Equation.3 . (11) We choose the coefficients a2, a3, b2, c1, c3, d2, d3 and s as variational parameters, and for the others, using relations (3-11), we obtained the following expressions:  EMBED Equation.3  , (12)  EMBED Equation.3 , (13)  EMBED Equation.3 , (14)  EMBED Equation.3 , (15)  EMBED Equation.3 , (16)  EMBED Equation.3 , (17)  EMBED Equation.3 , (18)  EMBED Equation.3 , (19)  EMBED Equation.3 . (20) The coefficients are given in order in which they are calculated. 3 Variational calculation of the dimer Having derived the trial wave function we performed a variational calculation  EMBED Equation.3 , (21) where  EMBED Equation.3 , (22)  EMBED Equation.3  is the reduced mass of 3He, m = 5.00649231( 10-27 kg and  EMBED Equation.3 . Than, the expression for the energy can be written in the form  EMBED Equation.3 . (23) For the interatomic potential we used ab initio SAPT potential by Korona et al. [6]. After adding the retardation effects (SAPT1 and SAPT2 versions) Janzen and Aziz [13] showed that SAPT potential recovers the known bulk and scattering data for helium more accurately than all other existing potentials. To calculate the integrals we used the Romberg extrapolation method [5] and by a minimization procedure obtained the binding energy of -0.014 mK. Values of variational parameters for this energy are: a2=2.873 , a3=3.698, b2=1.55 , c3=5.9, d2=573 , d3=2.0, s=0.0009318 -1 . The value of the parameter c1 doesn't affect the binding energy, but only the normalization integral, in our calculation it has the value c1 =0.03588. We also used the boundary points r3, r4, r5 and r6 as variational parameters. Their final values are r3=19.5 , r4=199 , r5=282 and r6=1200 . Other parameters, when calculated from the expressions (12-20) are: a1=0.01988, b1=0.01456, b3=0.547, c2=217.6 , d1=0.03588, e1=0.03634, e2=1262.9 , e3=3.634 and g1=0.05257. In the limit  EMBED Equation.3  the wave function has the asymptotic form EMBED Equation.3 , where s0 is determined by relation  EMBED Equation.3 . The value of s0 coincides with the value of s, what confirms the correct asymptotic behaviour of the wave function (. The function f(r) and its first derivative are shown in Fig.1. We also calculated the mean value of internuclear distance < r > and the root-mean-square (rms) deviation (r for the (3He)2.  EMBED Equation.3 , (24)  EMBED Equation.3 , (25) and  EMBED Equation.3 . (26) The obtained values of < r > = 651 and (r = 562 show that (3He)2 is a really huge molecule. Our results for the energy and average radius < r > confirm the results of the numerical calculations from the paper [2]. Since the value of our binding energy is a bit higher than the one in ref. [2], which is to be expected from a variational calculation, we also obtained a bigger value of average radius. This small energy requires a great numerical precision. To verify our numerical procedure we repeated the whole calculation, with a slightly redefined wave function and using an equivalent but different expression for the energy. Namely, the function f3(r) now reads,  EMBED Equation.3 ,  EMBED Equation.3 , (27) and the function f4(r) is defined for  EMBED Equation.3  where ( =1.1 . From the condition that the function and the first derivative are continuous in  EMBED Equation.3  two relations for parameters d1 and d2 are obtained,  EMBED Equation.3 , (28)  EMBED Equation.3  . (29) The relations for other parameters (13-20) are left unchanged. With the wave function defined in this way no singularities in the second derivative of the function ( are expected, and therefore the variational calculation can be performed using the relation (23) as well as the following relation for the energy  EMBED Equation.3  , (30) where the kinetic energy is expressed through Laplace operator, (. The minimization of energy in both cases gave the same value of - 0.014 mK, which is the same as the one obtained using the function where there is no displacement ( from the maximum in r4. Thus, we can be certain in applied numerical procedures. 4 Calculation of trimer with spin-1/2 In 1979 Cabral and Bruch [7] considered the binding of 3He2 and 3He3. They performed a variational calculation, with the interatomic potentials available at the time, and concluded that both molecules are probably not bound in 2 D. Our results for the dimer led us to extend variational calculation to trimer binding. Since 3He atoms are fermions they form spin-1/2 trimers and spin-3/2 trimers. The results from [7] indicated that spin-1/2 trimer has a lower energy and therefore we studied only that case. The chosen form of the variational wave function, following [7, 8] is  EMBED Equation.3 , (31) where Xs and Xa are spin doublets symmetric and antisymmetric, respectively, under exchange of particles 1 and 2 while (a and (s are space wave functions which are respectively, antisymmetric and symmetric under exchange of particles 1 and 2. Spin +1/2 projections of the doublets are  EMBED Equation.3 , (32)  EMBED Equation.3 , (33) where  EMBED Equation.3  are the usual spin up (down) eigenstates of a spin 1/2 particle and the subscript i is particle label. In the calculation for the space wave functions we combine the following forms:  EMBED Equation.3  and  EMBED Equation.3  , (34) then  EMBED Equation.3  and  EMBED Equation.3 , (35)  EMBED Equation.3  , (36) where f(rij) is the new dimer wave function (2), with the ( modification. The constructed wave function is antisymmetric under exchange of particles 1 and 2 and symmetric under cyclic exchange of particles 1,2 and 3. Therefore [8] it is also antisymmetric under the exchange of particles 2 and 3 as well as 1 and 3. The Hamiltonian of the system is  EMBED Equation.3 . (37) Again a variational ansatz was used to calculate the binding energy (21). Using the fact that the Hamiltonian is spin independent and symmetric under the exchange of x and y coordinates we managed to express energy by the following relations:  EMBED Equation.3  , (38) where  EMBED Equation.3 , (39)  EMBED Equation.3 ,(40)  EMBED Equation.3   EMBED Equation.3  , (41)  EMBED Equation.3   EMBED Equation.3  , (42)  EMBED Equation.3  (43) C is a constant,  EMBED Equation.3  ,  EMBED Equation.3  and ( is the angle between  EMBED Equation.3  and  EMBED Equation.3 . The fact that expressions for the energy were reduced to three-dimensional integrals enabled us to perform the calculations using the same numerical methods as in the dimer case. After time consuming numerical calculations we found that the upper bound of binding energy of 3He3 trimer was -0.0057mK. Using the same wave function we derived the average distance among atoms of  EMBED Equation.3 = 4503 and  EMBED Equation.3 = 3633 . 5 Discussion To the best our knowledge the function (2) is the first trial form which in variational calculation led to the binding of helium 3 dimer. In this case one-dimensional Romberg integration with high accuracy has been performed. The results are in good agreement with those obtained by numerical solving of Schrdinger equation. Having appropriate two-body function we were able to construct a special form of Cabral-Bruch trimer wave function describing state with spin 1/2. We performed a very accurate Romberg integration of three-dimensional integrals and found an upper bound to the binding energy of -0.0057 mK. This shows that helium 3 trimer with spin-1/2 is bound in two dimensions. (As it was showed in the paper [4] binding of diatomic helium molecules is significantly increased if they are close (about 3 ) to the surface of liquid helium. It means that binding of trimers could be experimentally observed in future.) This result is quite a new one. It opens the question of the phase of many helium 3 atoms on a surface of liquid helium 4. So far it is believed that they form two-dimensional gas. A qualitative estimation of our result for trimer may be done as well. The obtained values of  EMBED Equation.3 = 4503 and  EMBED Equation.3 = 3633 show that 3He3 is a large molecule. Let us assume that there is a homogenous monolayer gas (or liquid) with the average distance between particles as in helium 3 trimer, then its concentration is 4.9( 1012 m-2 . This concentration is several orders lower then one of 3%, what is the upper limit for the attractive interaction between two 3He atoms in helium 3 - helium 4 film [14]. Consequently, it may be concluded that in our case a necessary condition for binding of three helium atoms is satisfied. Recently, new interatomic helium potentials appeared. Van Mourik and Dunning computed a new ab initio potential energy curve [9] that lies between the HFD-B3-FCI1 [12] and SAPT2 [13] potentials, being closer to SAPT2 potential. Other authors [10, 11] conclude that, according to their calculations, SAPT potential is insufficiently repulsive at short distances. In the papers [2, 3] the binding energy of helium molecules was calculated using two different potentials, HFD-B3-FCI1 and SAPT. The obtained results didn't differ much for these two cases. Therefore, we don't expect that the calculations with new, more precise potentials would change our results appreciably. 6 Acknowledgements We are indebted Professor E. Krotscheck for many stimulating discussions and R. Zillich for providing us with data concerning numerical solution of Schrdinger equation for helium 3 dimer in 2 D. References [1] A. F. Andreev, Zh.Eksp. Teor. Fiz. 50 (1966) 1415-1419. [Sov. Phys.- JETP 23, 939 (1966)]. [2] S. Kili, E. Krotscheck and R. Zillich, J. Low Temp. Phys. 116 (1999) 245- 260. [3] S. Kili, L. Vranjea , Croatica Chemica Acta 73 (2000) 517-524. [4] S. Kili, E. Krotscheck and L. Vranjea , J. Low Temp. Phys. 119 (2000) 715-722. [5] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes. The Art of Scientific Computing (Cambridge University Press, Cambridge, 1989). [6] T. Korona et al., J. Chem. Phys. 106 (1997) 5109-5122. [7] F. Cabral and L.W. Bruch, J. Chem. Phys. 70 (1979) 4669-4672. [8] M. L. Cramer, L. W. Bruch, F. Cabral, J. Chem. Phys. 67 (1977) 1422-1449. [9] T. van Mourik, T. H. Dunnig, J. Chem. Phys. 111 (1999) 9248-9258. [10] R. J. Gdanitz, Mol. Phys. 96 (1999) 1423-1434. [11] J. van de Bovenkamp, F. B. van Duijneveldt, J. Chem. Phys. 110 (1999) 11141-11151. [12] R. A. Aziz, A. R. Janzen, and M. R. Moldover, Phys. Rev. Lett. 74 (1995) 1586-1589. [13] A. R. Janzen and R. A. Aziz, J. Chem. Phys. 107 (1997) 914-919. [14] R. B. Hallock, Physics today, June 1988, 30-36.  f(r) f'(r) r () Figure 1: The figure shows the radial wave function f(r) (solid line) and the first derivative f'(r) (dashed line) of helium 3 in 2 D for the parameters determined by minimization of the energy. SA}ETAK Varijacijska analiza dimera i trimera helija 3 u dvije dimenzije L. Vranjea i S. Kili Varijacijskim prora unom dobijena je energija vezanja dimera helija 3 u dvije dimenzije. Postojanje jednog vezanog stanja, s energijom vezanja od -0.014 mK je definitivno utvreno. Takoer je odreena energija vezanja odgovarajueg trimera spina-1/2 od -0.0057 mK. Ovaj rezultat otvara dvojbe o tome da atomi helija 3 formiraju plinsku fazu na ravnoj povraini suprafluidnog helija 4. PAGE 1 PAGE 9 8JKPQgh  b c f g   8 9 D E e f $%5^¹ jUmH sH 5B*CJhphB*CJH*hph5B*CJhphB*CJhph5B*CJmHphsHB*CJmHphsH6B*CJmHphsHB*CJ mHphsHB*mHphsHmHsH8\68f$a$$a$PMMM 345]^$a$NORSؾششتتᙒ}le jxEHU!j*C< CJUVhmHnHu jEHUjcA< UVmHnHu jEHU!j=B< CJUVhmHnHu5B*CJhphB*CJH*hph jgB*CJhmHphsH6B*CJhphB*CJhphmH sH  jU jEHUjT>< UVmHnHu'J|Qo$Cb2Qp$a$-./023FGHIKL_`abdexyz{}~~mf jEHU!jU< CJUVhmHnHu jEHU!jpU< CJUVhmHnHu jEHU!jU< CJUVhmHnHu jEHU!jZU< CJUVhmHnHu j EHU!jT< CJUVhmHnHu j EHU!jT< CJUVhmHnHu jUmH sH ' !"+,-789CDEOPQopqtuvyݴݜ݌xxxxxxxxB*CJH*hph6B*CJhphB*CJhph j EHU!jV< CJUVhmHnHu jEHU!jV< CJUVhmHnHu jEHU!jV< CJUVhmHnHumH sH  jU jEHU!jV< CJUVhmHnHu/yz{~./056778K⿬5B*CJhph%j"B*CJEHUhmHphsH#j?Y< B*UVmHnHphu!jB*CJUhmHphsHB*CJhphB*CJH*hph6B*CJhphGEHU!j`d< CJUVhmHnHu jCDEHU!jc< CJUVhmHnHu j}AEHUj_< UVhmHnHu j?EHU!jM_< CJUVhmHnHu jU 5mH sH  6mH sH mH sH  H*mH sH *   !"#*q#ng jqYEHU'jq= B*CJUVhmH phsH 5B*CJhphB*CJhph jVEHU!ji< CJUVhmHnHu jxSEHU!jh< CJUVhmHnHu jPEHU!jl< CJUVhmHnHu jSMEHU!j2h< CJUVhmHnHumH sH  jU& *opq-. ":#;#z###$8$<$[$%%$a$#$%&-./BCDE]^bdpqtxԱԔԊzԔhU%jr`B*CJEHUhmHphsH#j< B*UVmHnHphu jB*CJhmHphsH6B*CJhphB*CJH*hph%j|^B*CJEHUhmHphsH#jw< B*UVmHnHphu!jB*CJUhmHphsHB*CJhphmH sH  jU j[EHU!jFn< CJUVhmHnHu(CItu        & ' ( / 0 < > ? \ ] _ !!! ! ! !>!?!@!I!J!K!S!T!U![!\!ѽѽdzdzdzdzdzdzѩdzdzdzdzdzdzdzdzdz56B*CJhphB*CJH*hphB*CJH*hph5B*CJhph6B*CJhphB*CJhphmH sH  jU jbEHU'jq= B*CJUVhmH phsH >\!a!c!d!!!!!!!!!!!!!!!!!!!!!!!!""""""-"."A"B"C"D"n"o""""""""""~%jgB*CJEHUhmHphsH#j< B*UVmHnHphu%jeB*CJEHUhmHphsH#j߬< B*UVmHnHphu!jB*CJUhmHphsH5B*CJhphB*CJH*hph6B*CJhphB*CJhph1""""""""""7#8#H#I#J#K#L##################uiu]XmH sH 5B*CJH*hph5B*CJH*hph5B*CJhph! jD6B*CJhmHphsH56B*CJhph! jY6B*CJhmHphsHB*CJH*hph6B*CJhph!jB*CJUhmHphsH%jiB*CJEHUhmHphsH#jஜ< B*UVmHnHphuB*CJhph!##$$$$$$.$/$0$1$=$>$Q$R$S$T$[$r$x$$$$$$$$$$$&&&ui]6B*CJH*hph5B*CJH*hph5B*CJhphB*CJH*hph! jD6B*CJhmHphsH6B*CJhphB*CJhph j4qEHU!j䂝< CJUVhmHnHu jnEHU!j< CJUVhmHnHu j5lEHU!j< CJUVhmHnHumH sH  jU!&&&&'''''''$'%'8'9':';'Y'j'k'l'm'n'o''''''''''''ƿܰᓎ|p_! jd6B*CJhmHphsHjxB*EHUph#j;< B*UVmHnHphu B*phjB*Uph6B*CJH*hph jvEHUjw< UVhmHnHu jsEHU!j< CJUVhmHnHu jUmH sH B*CJhph6B*CJhph56B*CJhph"%'Y'I(h(())+++E+F+G+--..///!0&0?0C0b0011$a$$a$'' ( ( ((.(/(2(7(8(;(I(J(K(^(_(`(a(i(j(}(~((((((((,)嶬嶬姞qf\\5B*CJhphjEHUmHsH!jᇝ< CJUVhmHnHuj|EHUmHsH!j< CJUVhmHnHujUmHsHmHsHB*CJH*hph6B*CJhph%jzB*CJEHUhmHphsH#jk< B*UVmHnHphuB*CJhph!jB*CJUhmHphsH,)-))))))))))!*"*$*******+E+G+~++++++++,,--------ֱֽ֦֫֘~~mf jͅEHU!j< CJUVhmHnHuB*CJH*hphB*CJH*hph 5mH sH 5CJmH sH  H*mH sH  jd6 6mH sH  jD6 jEHU'jVr= B*CJUVhmH phsH  jUmH sH 5B*CJhphB*CJhph! jY6B*CJhmHphsH(------- .!.#.'.(.*............../ / // /!/"/9/˵˝s`%jB*CJEHUhmHphsH#j< B*UVmHnHphu!jB*CJUhmHphsH jŠEHU!j< CJUVhmHnHu jEHU!j< CJUVhmHnHu jUmH sH ! jf6B*CJhmHphsH6B*CJH*hph6B*CJhphB*CJhph!9/:/>/?/u/v////////000000'0(0;0<0=0>0?0D0E0X0Y0Z0[0c0d0w0x0y0z0xg` jQEHU!j< CJUVhmHnHu jYEHU!jg< CJUVhmHnHu jiEHU!j< CJUVhmHnHu jEHU!jE< CJUVhmHnHu jEHU!j< CJUVhmHnHu jUmH sH 6B*CJhphB*CJhph5B*CJhph%z00000000000011111112E2I22222222 3 3 333313233343<3=3P3qj jrEHU!j͞< CJUVhmHnHu j EHU!j-͞< CJUVhmHnHu jZEHU!j̞< CJUVhmHnHu jU! jd6B*CJhmHphsH5B*CJhphB*CJH*hph56B*CJhph6B*CJhphB*CJhphmH sH )12233<3Y3q33333:6;6<6=6>6?6O6P6Q67:H=>???@$a$$a$P3Q3R3S3Y3Z3m3n3o3p3r3s333333333333333333333333Ŵń}xxg`x jiEHU!jӞ< CJUVhmHnHumH sH  jqEHU!jBҞ< CJUVhmHnHu jEHU!jў< CJUVhmHnHu jEHU!jӞ< CJUVhmHnHumHsH jNEHU!jў< CJUVhmHnHu jU jEHU!jϞ< CJUVhmHnHu"3333 4 4 4444%4&4'4(4-4.4D4E4X4Y4Z4[4`4a4t4u4ɶ중n[I#jԞ< B*UVmHnHphu%jB*CJEHUhmHphsH#jԞ< B*UVmHnHphu! jq6B*CJhmHphsH%jB*CJEHUhmHphsH#jԞ< B*UVmHnHphu%jKB*CJEHUhmHphsH#jdԞ< B*UVmHnHphu!jB*CJUhmHphsHB*CJhph6B*CJhphu4v4w45555556 6 6 666-6.6/606?6Q6x6y6z6{699|9}999 ; ;;;ҾҬ҇tj`````Ҭ5B*CJhph5B*CJhph%jB*CJEHUhmHphsH#j֞< B*UVmHnHphu%jB*CJEHUhmHphsH#jK՞< B*UVmHnHphuB*CJH*hphB*CJH*hphB*CJhph!jB*CJUhmHphsH%jB*CJEHUhmHphsH"; ;!;/;0;C;D;E;F;Z;[;];_;;;;;<<<<<<!<<<<<==?@@@AAAAңҙҏҏңuiңҙu__ҏҏ5B*CJhph6B*CJH*hph6B*CJhph jB*CJhmHphsH5B*CJhphB*CJH*hphB*CJH*hph%j|B*CJEHUhmHphsH#j֞< B*UVmHnHphuB*CJhph!jB*CJUhmHphsH%jB*CJEHUhmHphsH%@@@@@@@@@@0AFAGABBB8C:CCC>DDDDDD.E/EEE$a$AA A5A7A=A>ABADAxBBBBBCC:CCCCCCCCCDwDxDyDDDDDDDDDEEEE!E"EiEkEmEnErEsEEEEEEEEEEEEEAFDFEFFFJFKFFFFFFFFFFF6B*CJhphB*CJ\hph5B*CJhmHphsHB*CJhmHphsH5B*CJhphB*CJhphKEEEEFMFbFcFFFFGGEGFGGGHGIGJGKGLGMGNGOGPGQGRGSGTGVG$a$FGGTGUG4H6H8H>HRHTHHHHHHHHHRIzIIIJHMJMNMPMRM^M`MbMdMfMjMlMxMzM|M~MMMMķ0JmHnHu0J j0JUmHsHB*CJhmHphsH5B*CJhmHphsHB*CJhmHphsH5B*CJhmHphsH6B*CJhph!jB*CJUmHnHphu5B*CJhphB*CJhph*VG]GeGfGgGhGiGjGkGlGmGnGoGpGqGrGGGPIRITIVIXIZI\I^I`IbIdI$a$dIfIhIjIlInIpIrItIvIxIzIIIIJJ@JBJHMJMLMNMPMfMhMjM&`#$$a$$a$$a$jMMMMMMMMM$a$&`#$. A!"#$%@=%\)ێtY%)z+4]X9r%x|,QĊ(Q0!`AA1 XM@Bk Ho!J  K $)iD"P-?f E5F1&Y3g Ƒ &k)i5ԦVA(꠺d$YN=EQOh;=Czd ,YL=3©>YD5<!"G8%2{̡sjLf13jʼFs,3 ©x oRSp֪&$ 5jJMunFSͩqT 2k+FՊfރւ6dזD3#2á7 :rC]nՉwAYc Յ@uC7~U}FIzS'Kzhk'4P]]`Fg,1D % qR :BHh;0J=5Zb ז+115ޠ5S]DId0Ņ1T i&bMpaA3j&Xk"N< X`a!DjM B K-,sa u_JVڅ56u:۰$6ڰMmJ}>iM[=ٔ¨$Ehݦn酏ܐ]n=n}n8Cn:4:1;nz(ŵgKW<*ʦs_s>gNF\:Sit﹮\7G;oNOI\Mr>I_I?A 5@2Pg1_2w2L0R׉KtF#\`O=O_dXon`<\Ә2QbɜL %iTIX2]gUZc`ܤ1 ̥pq:@*^g>ܬ@PgWJYL$-Kˠr Vn*[mPQYVvezJJ]'~$;MN.Y}n:= UR%v@e:iGҸ_-G39s08s H uC%> TD#)ACGOg%>ĹTs1 +Y&%4J"}-qA'oM\V^ĿOBH\hsŠįI=WwS\zZΟ&[T=J]'mĄ=QBRq%n2@k1рYryhUйmTC"wĝ&"aw[G%^#/K/QEUUոjPa X^xB ר$P{]'L+!.xC#D uMׄk*/hhފ؋ͤLR͕F64vԫ.&Ւz݅p L[R5޶Ćf647h+BKZI3hm-(m)uFlzG:Xu]:D]S]lB7NRC*^.&mtSR_uϠA7 0Mj 4TwSClRa6 wKO*#lIz-mQ6$Җ1N6Gcƻ/5 mGMd+S4նR1nf@Xu Y`nmT6̥x1- |h!E|8= 5+DD۶I^y Yh/$ovRk}lm㼶g۲$IM(P %97іMdm DW&~}PDl:ѷs4[Q)b v>3M:qN鱏Y^Knfܮ"h7s׹sM)⼲s˾"#uȎ/P:-*BuMFbkqJ%7D)u:WvXvZNߐK+cb nU8^lvNܽXs]|\$Y>[dK*d:)6m*62 b@]'㳒}">_f-~[>N٢HYJ]5l/t~1u:(m~N9uxz "礟ϩY~~.dS:):S~"B]']GqqƯqN|OuvpPIaQ\|w9gCp` 窢.%ך$uD= Il!c`6H,&Q< % KB V$A2Id mT K>r48H9 H#!8J>Ag!|c$ }7"|LC? ]B92~W?U'dARPIIJL*ͨ,SG Vt9E*ۙJt' ܃E S&0Ѓ!:0z1cLMTy3!Lm&2O2O1O30gL LCE&yI2ӈi,xyyM yC&mAAS ݌i.h!hɝ!mmttI!,EUMNO^::}t3@g C$J .3BbN40%h1c%Y/1A"}$%0U"4&LL61\q6̳oaZXdS.,R \Xn"`v| +]Xjذ lXolh&7m)D zo~܊EfT*WpΔ!{UF'>>aL#G!#a9%s@KE='[0\@I_GmRxRp?EӇl%S }Pc/)0a/nG4ˍ}hM_Y_shl6l>d+af:l<:Hn{[=5ދZXIBI$ԚjMO–$jMTVkPk*n ZSS%ՃZS5՚.Ԛ[BttlIt/juZBr:Xz80k˚ eM .&xȚIJ&IY ?)̚IJ&IY0kIjQi)ks"U0N!u9YKMVm;:<^[رNa4XiұNi.ucòHYs0k5e͑`Ys/w{VkD,;ޱm+Xvb!pYD)k"fM&RD̚"k,k5&KYYd)k2fMv5C5EʚYS),k5Ț!k*˚*eMŬRT5UʚYS]dM5eMct)k:˚.eMǬ.{ȚɲfJY ޵[5e͔fbLY3=dfY`.̚ͲfKY1kek g5?orVZ#O*ֈX6OSy{.ZP| ]uZN _RH9v˳>V` jלgp 2$2ƐiЛ̆d4"u 'qPlmNv@U&{ UALC%r'PBo8i>_#O g; srxN^?k} ?-h[qemY'1T=|<ΣAELz9IBL~OU&b5=xkvå2 .';jv@WT ]Gu- ᑩJ ףfGLN6duɛ-dUC݊G6TEkvAVSwWAs'YIEVd9u_d)K-I-d! Y@=DSW[Ijԣd#4Qd85̀''t4 b&SgY2YxL{6q"+c*^Fk(r# jM P g=JdUJ'C"M2 %1$MH<􁷅LͅT ݡN7Օj-t6:q݀ t:A{XБ(%$AgN'jӅJ鴂:-BOcҋ0-44: [ BcaP0؏B;Zg֡GF*2ҤcB"Ud$X oR`aI6&[SGii6[ac&4ˡ61Flcޝ;xH}~,cKX,w`+XjhC):;fww&MfiwmH Nvhwׅ}Bޙ8eݱttЅC.Uґ ;8n;n3u;i;+}Xwsգ<:ԇӒBCM#!|LKh,|_ec^Y>co]|BKKVКZh#|#M3ht<X;$NEf~AB/e+-ChXɺhI_xM_23Cg'l0DK*$0H0 c:IBXqy:%|BEjdaT5`:\3C"LYBejbaA2\b2O2,,.),˄%&,ӹ·`No%Ż;s;9V\IQX W ) &$kt6lku6\,yWa Tj6T|vHvB5]&{ & M&itpACpa#P]8pLPԹ:np¤$K%>^QrMIC#M/O.ORw )|s\/R¿o"}1N{~ ~4y (=t~3]a _+a?ǻ;SǛYw  >Qr-TyL8O| I*<.\p .yRbp˨L.WB• WY_#b [mf6"^P]:w۸+ qΫ:kau?jYzzc~D ~@HZ:NΎh̺S8/ΤIuFR[K=W; H{ #?` tiud;q;<8Igh3ptoG몔1uSJ ӝ,֝D3Iߠ%;3E;VdGsIKH|A"y;j֝9dI@4(- lE sdeXPVΌqjpG֔()1JXWJF :;3pºcDbm 1l*6[J*q5l q᝙v֝@5η5hƻ^ٶb31RKdR1᝙n֝`kOvUjL+rwwfXwT=ڌb, J&Ywlw2kNJ 䀥{_2ϱes9I|h/,JĢsqZ ޙ8e t[bqTXܓAǻ; c;E?@+U%wwf-;%k?ܚ2#H-xwxgֱu8"!6Fs?%i}ɆqGxwxg6Kqsɦ[CY3['^-q'ʄ-!m 2ޙmRw轐m xwxgv >]뎛zCIOv ޙ]Rwv9! ] ;%ͫ!A'D'u'rNǻ;&u2)ri!A'f"A;vK)VBJA;3pbݱ{Y!ġOxwxgH  GBww<R :ޙL;~FHe ;%)N;3YRwJ:[Yq2 ޙSRw )xwxgNK)lz?pɖSʊB9h ;yζQ݊*<_utcGT~4P3Npd0L$#7IkMDӠ Id$aY+*H!)dl%[`Iv.4K>rF2qH'YpB } :>C\8BD_o(G#?_Я(~G@>d|<$yLEt.D1T].# & ]BWkku*s=Uc r#sTgnE( ܃j221A!a(<.yyyyyyV8gqߋ,GvZDd HkB  S A? 2<ȁv)LDp`!ȁv)L@j"x=OAggט;;JRH(ɤ:RR` pgSaĝ !LM QDIQS>&)r3{w } ]);؁J$I\fL L3خTj/F=9x AZv4r'vh𢲶0S_"e r]C Kh]mutODjX]6-ݽRټcLε#}\xsv0$ظc)h|^_^9>Onޗ[W?|}7O_]VxT g 3d|@뙿y=Ov}'=O:j\^oje `wT>; z}U'&圯|Os3hxO0J::W9vᔶQv{ִLBOB/oU>SCzm-}玄dDd rB  S A? 2Y?oYºZXJ5p`!-?oYºZXJ@xTKA~f~͞w1XHH@ \R')NӨxw!w"gt6W҄t$GDkDDΛ]}ߛ{۷0H*xJ#E\Ș0HeFYAeƐ@ h0~Hy\srsTƇ21gt (:x=ď[vc3îKfY߭t2:g#m%tc$l ahg[XC<~):\,fiغICGy秚w%@큐LײD9 u\츫ѷzn;؟z7'b'O/VMy%,*U/TOo+5jӞp`!7>5jӞ`@"x+Q9wVvvXQ4)"!?(xQeb)yP^ <([Ƀ-{"3ݙ=s^(xB*+"Gr D5ij5Ah1/2/VcQj d'(|(=98 3ÙG dI{UVlEveBZrۜɻl(Hi_bt7Rd |>5sPO3Y|>5ﭿ[Mbc~1 $?,db`MwTm𬄝 y؈0wX΂?hV&ޕ"!`yVu]-dn*Ye*Y+křTY0QՑ?s>q򹖾AlMkNNj]_:pg2 ?JWRa#DdTB  S A? 2x9{*|˽ö5ip`!ax9{*|˽ö5 XJ/xcdd``gd``beV dX,XĐ I A?d-@P5< %! `~}vL@(\_(-n&R#Ƃ}I?B? PHfnj_jBP~nbC3&=`ei2٘A|C 5ݍ &`H%n,2m |L7 `7c-8^)Jm@b121)W2Cw33XkdwQDdhB  S A? 2߯rѬW p`!߯rѬW @x|]xcdd``.ed``beV dX,XĐ Ɂ A?d jx|K2B* R.ͤ `W01d++&10D(yA|\  |y 6/`\ &'/RS Rpvk`o!v3BMzϰ' L;$?/󟱠;273iF O& Ma` p!fߖ Ni =P;D@)#RpeqIj.;t?2Ak#DdhB  S A? 2涅r2R1'xGi0 p`!a涅r2R1'xG@ |/xcdd``gd``beV dX,XĐ Ɂ A?d-@eOjx|K2B* R*3 P 27)? d.PHq1ZM>F? d)7~br<: &1BMzΗb&7#dt760na#nl`_ʄʷa0LDh60rt \{j(PyĤ\Y\`ueDd pB   S A ? 26( ?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{}~435Root Entry F,Data |iWordDocumentObjectPool`),_1016872532F`)`)Ole CompObjfObjInfo "#&),/0147:=>?BEHKLMPSVY\_bglopqruxyz{~ FMicrosoft Equation 3.0 DS Equation Equation.39qوkIvI =1 r  exp"ar()  "sr[]Equation Native _1016873533 F))))Ole CompObj f FMicrosoft Equation 3.0 DS Equation Equation.39q٨$vIpI (r)=1 r  f(r)=1 r  f i (r) i=16 "ObjInfo Equation Native  _1016873315 F))))Ole CompObjfObjInfoEquation Native _1016873770F))@Q* FMicrosoft Equation 3.0 DS Equation Equation.39q٨$vIpI f 1 (r)=a 1 exp"a 2 r() a 3 []Ole CompObjfObjInfoEquation Native d FMicrosoft Equation 3.0 DS Equation Equation.39qHkIvI r"r 1 ,r 2 [] FMicrosoft Equation 3.0 DS Equation Equation.39q_1016878235'F@Q*@Q*Ole CompObjfObjInfo ӌI8mI f 2 (r)=b 1 (ln(r"b 2 )) b 3 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native !_1016878219F@Q*@Q*Ole $CompObj %fObjInfo!'Equation Native (d_10168784266$F` *@*Ole *H`~II r"r 2 ,r 3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qӼX{II f 3 (r)=c 1 exp"r CompObj#%+fObjInfo&-Equation Native ._1016878363)F@*@*4 "rc 2 () c 3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qHԛII r"r 3 ,r 4 []Ole 2CompObj(*3fObjInfo+5Equation Native 6d_1016878448.F@*@*Ole 8CompObj-/9fObjInfo0; FMicrosoft Equation 3.0 DS Equation Equation.39qӼ\I|I f 4 (r)=d 1 exp"r"r 4 d 2 () d 3 []Equation Native <_1016878573,;3F@*@*Ole @CompObj24Af FMicrosoft Equation 3.0 DS Equation Equation.39qHDIuI r"r 4 ,r 5 [] FMicrosoft Equation 3.0 DS EqObjInfo5CEquation Native Dd_10168787771E8F$*M=*Ole FCompObj79GfObjInfo:IEquation Native J_1016878749=FM=*M=*uation Equation.39qӼhII f 5 (r)=e 1 exp"r"r 4 e 2 () e 3 [] FMicrosoft Equation 3.0 DS EqOle NCompObj<>OfObjInfo?QEquation Native Rduation Equation.39qH`~II r"r 5 ,r 6 [] FMicrosoft Equation 3.0 DS Equation Equation.39q_1016878803BFM=*tF*Ole TCompObjACUfObjInfoDWEquation Native Xp_1016878841@JGFtF*tF*Ole ZCompObjFH[fTI@I f 6 =g 1 exp("sr) FMicrosoft Equation 3.0 DS Equation Equation.39q<xItI r"r 6 ,"[]ObjInfoI]Equation Native ^X_1016879423LFtF*tF*Ole ` FMicrosoft Equation 3.0 DS Equation Equation.39q$kIvI r=r 4 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjKMafObjInfoNcEquation Native d@_1016879456"wQFN*^*Ole eCompObjPRffObjInfoShEquation Native i@$II d 2 >1 FMicrosoft Equation 3.0 DS Equation Equation.39qkIvI a 1 exp"a 2 r 2 (_1016879553VF^*^*Ole jCompObjUWkfObjInfoXmEquation Native n _1016879687Tc[Ff*f*Ole sCompObjZ\tf) a 3 []=b 1 (ln(r 2 "b 2 )) b 3 FMicrosoft Equation 3.0 DS Equation Equation.39qlIlI a 2 ObjInfo]vEquation Native w8_1016880133Ym`Fo**Ole |r 2 () b 3 a 2 r 2 =b 3 r 2 "b 2 1ln(r 2 "b 2 )F FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj_a}fObjInfobEquation Native 8_1016880107eF**PI8mI b 1 (ln(r 3 "b 2 )) b 3 =c 1 exp"r 4 "r, 3 c 2 () c 3 []I FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObjdffObjInfogEquation Native T8II b 3 r 2 "b 2 1ln(r 3 "b 2 )=c 3 c 2 r 4 "r 3 c 2 () c 3 "1_1016880167jF**Ole CompObjikfObjInfol FMicrosoft Equation 3.0 DS Equation Equation.39q0II c 1 =d 1 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native L_1016880227hroF`9*`9*Ole CompObjnpfObjInfoqEquation Native h_1016880355tF`9*`9*Ole L{IؑI d 1 exp"r 5 "r, 4 d 2 () d 3 []=e 1 exp"r 5 "r, 4 e 2 () e 3 []CompObjsufObjInfovEquation Native p_1016880559^yFژ*ژ* FMicrosoft Equation 3.0 DS Equation Equation.39qTII d 3 d 2 r 5 "r 4 d 2 () d 3 "1 =e 3 e 2 r 5 "r 4 e 2 () e 3 "1 FMicrosoft Equation 3.0 DS Equation Equation.39q$vIpI e 1 exp"r 6 "r, 4 e 2 () e 3 []Ole CompObjxzfObjInfo{Equation Native =g 1 exp("sr 6 ) FMicrosoft Equation 3.0 DS Equation Equation.39qӴНI8mI e 3 e 2 r 6 "r 4_1016880645~F@* ˲*Ole CompObj}fObjInfoEquation Native _1016880973|F@l*@l*Ole CompObjf e 2 () e 3 "1 =s FMicrosoft Equation 3.0 DS Equation Equation.39q0t~IzI d 1 =c 1ObjInfoEquation Native L_1016881032F@l*@l*Ole  FMicrosoft Equation 3.0 DS Equation Equation.39q XII b 3 =a 2 r 2 () a 3 a 3 r 2 (r 2 "b 2 )ln(rCompObjfObjInfoEquation Native (_1016882116F** 2 "b 2 ) FMicrosoft Equation 3.0 DS Equation Equation.39q<kIvI c 2 =(r 3 "b 3 )ln(r 3 "b 2 )c 3 Ole CompObjfObjInfoEquation Native Xb 3 (r 4 "r 3 ) c 3 "1 [] 1/c 3 FMicrosoft Equation 3.0 DS Equation Equation.39q pIDmI b 1 =c_1016882272F 5**Ole CompObjfObjInfoEquation Native <_1016882845F**Ole CompObjf 1 exp"r 4 "r 3 c 2 () c 3 [](ln(r 3 "b 2 )) b 3 FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoEquation Native (_1016883250F%*%*Ole  II a 1 =b 1 (ln(r 2 "b 2 )) b 3 exp"a 2 r 2 () a 3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfoEquation Native _1016884397F%**pЙIDI e 3 =lns(r 6 "r 4 )[]d 2 r 5 "r 4 () d 3 1d 3 lnr 6 "r 4 r 5 "r 4 ()Ole CompObjfObjInfoEquation Native  FMicrosoft Equation 3.0 DS Equation Equation.39qkIvI e 2 =e 3 s() 1/ e e  3 (r 6 "r 4 ) 1"1/ e e  3_1016883389OF**Ole CompObjfObjInfo FMicrosoft Equation 3.0 DS Equation Equation.39q,{IDmI e 1 =d 1 expr 5 "r 4 e 2 () e 3 "r 5 "r 4 Equation Native H_1016883656F**Ole CompObjf    #&)*+,/47:=>ADEHKLMPSVYZ[^adgjorstux{|}d 2 () d 3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qlIJ g 1 =e 1 e  e@sr  6 expObjInfoEquation Native _1025339792lFX+!+Ole  "r 6 "r 4 e 2 ()  e@e  3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qӜII Ed" CompObj fObjInfoEquation Native _1016884806F!+!+* 2H r  dr  +"  * r  dr  +" FMicrosoft Equation 3.0 DS Equation Equation.39qӌkIvI 2H ="! 2 2+2V (|2r  1Ole CompObjfObjInfoEquation Native  "2r  2 |) FMicrosoft Equation 3.0 DS Equation Equation.39q kIvI =m/2 FMicrosoft Equation 3.0 DS Eq_1016899703F@I(+@I(+Ole CompObjfObjInfoEquation Native <_1016899837F@I(+@I(+Ole CompObjfuation Equation.39qLkIvI r=|2r  1 "2r  2 | FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfo!Equation Native "h_1025339844F`/+@@+Ole $CompObj%fObjInfo'Equation Native ((_1016900831FI+I+ II Ed"rdr(V(r) 2 (r)+ ! 2 2 ("(r)) 2 ) 0" +" rdr 2 (r) 0" +" FMicrosoft Equation 3.0 DS Equation Equation.39qOle -CompObj.fObjInfo0Equation Native 14kIvI r!" FMicrosoft Equation 3.0 DS Equation Equation.39q8ܓII e " e s  0 e r_1016901033FI+I+Ole 2CompObj3fObjInfo5Equation Native 6T_1016901344F |Q+ |Q+Ole 8CompObj9f FMicrosoft Equation 3.0 DS Equation Equation.39q|dItI  e@s  e@0  e@=  e@  e@2  e@!  e@2(") ObjInfo;Equation Native <_1016955528F |Q+Eb+Ole ?CompObj@fObjInfoBEquation Native C_1016955560Flk+lk+ FMicrosoft Equation 3.0 DS Equation Equation.39qPԜkIvI <r>=r 2 (r)rdr  +"  2 (r)rdr  +" FMicrosoft Equation 3.0 DS EqOle FCompObjGfObjInfoIEquation Native Juation Equation.39qPԸܮII <r 2 >=r 2  2 (r)rdr  +"  2 (r)rdr  +" FMicrosoft Equation 3.0 DS Eq_1016955620Flk+lk+Ole NCompObjOfObjInfoQuation Equation.39qP\ II (r)= <r 2 >"<r> 2 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native Rx_1016956863&F s+ s+Ole TCompObjUfObjInfoWEquation Native X_1016956023F s+ s+Ole \P0vI|I f 3 (r)=c 1 exp"|r 4 "r|c 2 () c 3 [] FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj]fObjInfo_Equation Native `l_1016956475F5|+5|+PPНI8mI r"r 3 ,r 4 +[] FMicrosoft Equation 3.0 DS Equation Equation.39qPP`~II r"r 4 +,r 5 []Ole bCompObjcfObjInfoeEquation Native fl_1016956523F5|+5|+Ole hCompObjifObjInfok FMicrosoft Equation 3.0 DS Equation Equation.39qP$IdI r 4 + FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native l@_1016956803Fփ+`ǝ+Ole mCompObjnfObjInfopEquation Native q _1016956897F`ǝ+`ǝ+Ole vPkIvI d 2 =d 3 c 3 () 1/d 3 c 2  c 3 /d 3  1"1/e 3 FMicrosoft Equation 3.0 DS EqCompObjwfObjInfoyEquation Native z_1025339990Fh+`1+uation Equation.39qPkIvI d 1 =c 1 d 2 () d 3 "c 2 () c 3 [] FMicrosoft Equation 3.0 DS Eq      !"#$%&'()*+,-./012o6X78:9;<=>?A@BCDEFGHJIKLMNOPRQTSUVWYZ[]\_^a`bcdegfhjikmlpqrstuvwxyz{|}~x+Aǟy}}f6AV9 DePAm݅R\Nϒ5"6|}3 xA#PEw,KtdL0 Ptf9ҋL{{a τu"i OM&b"*6b \j%>6≏ӹy@eP-}ɥG9i+.i>dߍ>SM`QNڊ^c>RKX4ovo>;W| Gc)>w(qAyJeuKu" `eUQҳ#QZ)WӼ9_sĽ=;k$LGteNU\XڢBN{r?Nw_3Q5wԺ~ֹfڹL [>} W:WLYNPAV Cl/Yx-~Χc#DdhB   S A ? 2 +F|9Y[ip`!a +F|9Y[@ |/xcdd``gd``beV dX,XĐ Ɂ A?d-@eOjx|K2B* R*3 P 27)? d.PHq1ZM>F? d)7~br<#0@Lbq H / CMnGnl`\6I$Fvc o `l`4n2LPj=󎑉I)$5Sf7Dd pB   S A ? 29-ltpnLIBp`! -ltpnLI8@x+Aǟy}Z~F9B,rR8X7WB-'9N~gf}my{<ߙyfA7@ PF,"cɞ.d/]@RXeD|.@puOFVsK@';*&b;SW9;dU k"F^(m O2@eTdǚ˻f䤭)~39i+~0zwfEs>jnDF},ŷFZsG5|( N/A]`gw[sDzE+Uad*=+Hԭyߺ+4o^9qkduYϔDLQYGs)YeýN1*w 7x"E͔ue.?2ĦtnelΝ#DdhB   S A ?  2-{*U7y'ip`!a-{*U7y'@ |/xcdd``gd``beV dX,XĐ Ɂ A?d-@eOjx|K2B* R*3 P 27)? d.PHq1ZM>F? d)7~br<F &1BMzΗbM&7#dt760na#nl`_ʄʷa0LDh60rt \{j(PyĤ\Y\`uceDd pB   S A ?  26b7ʉ-&/+X4p`! b7ʉ-&/+X8(x+EAϜ{xy~nY++C(ކ,Rdc,5gfw)2|9gfDx5G(%dG HT#-Ȍw ?uq:giC ABe_)]c'CX ZZK]Ҫ("fߵ*I f#ӓZ "aN9swW_[}S|exw?.BjdIü-4_Zs x#n4q .'R ^WWCi0]a$j3%ĭWpp/:-#D_#a&Sr/gl'[PkȚ3${P6G1=ݫZ~t"m c[窛 ]e5y? ߳N#DdhB  S A?  2ק Ťo_Qkip`!aק Ťo_Qk@ |/xcdd``gd``beV dX,XĐ Ɂ A?d-@eOjx|K2B* R*3 P 27)? d.PHq1ZM>F? wf)7~br<: &1BMz aM&7#dt760a#nl`_ʄʷa0LDh60rt \{j(PyĤ\Y\`u_e]!Dd|hB < S A:?  2sdEC:~>*g#p`!_sdEC:~>*@` @|-xcdd``V`d``beV dX,XĐ Ɂ)KRcgb SFnĒʂT ~35;a#L ! ~ Ay GA.si#I Ś ߀X@*R+ 4 f*'LF/?~f0\Hе]qo ).⧁C-\P 27)? AJu`72pAC C !A= cdbR ,.Iexf:=WKDdhB = S A;?  2J5A3x 40`D p`!XJ5A3x 40@ |&xcdd``vgd``beV dX,XĐ Ɂ A?d-@eOjx|K2B* R*3 P 27)? d.PHq1ZM>F? e)o@^~FF#ҥp>'#h1 M-VK-WMc` M:Pk0M2p#nZ "8߆%8N(uP yĤ\Y\ݵ`ucjDd0TB > S A<? 2[?M[?7^"p`!/?M[? kXJxcdd`` @bD"L1JE `x,56~) M @ k);030j䆪aM,,He`7C&0] ZZ r.PHq=`v Ԅ0 I `|_dpMMa`b#\) \PsC5"8=p|Ĥ\Y\ݍ`uiBDdTB ? S A=? 2biъt>O$p`!6iъt @2XJxcdd`` @bD"L1JE `xX,56~) M @ k)`f`8 UXRYvo`0L`A $37X/\!(?71a!%@y m( Rl5A?&0nF F&#I9 L0@3] ; 0Fs.hXq%D@{@1I)$5rKDdp pB @ S A>? 2WǙ~|U3!3G&p`!+Ǚ~|U3!zS!xKA߼ٽ~WpXJrN8a![(u iRO c!!M !]J[$‘BLͼys]233o;{rz)rTG!8ȄG(Lvۺ"Fn4ЯL/T &xTQ'j)Z09E?_lnԆg/>PTRQ+KޢskF_?lOW2+E@O}~Igi)W ϊ\Re[X˦Wz8[/'Jdhpe4G#B(\NĝjhVipI|!w㮙qܗٗv帐|>$a#Õv-4åw[> u.1<,\qo  V*[}+.33A>4</] Oϭw߶>2hK -4փZg@꼿hqDd| B A S A?? 29 -Uh˯0s4)p`!  -Uh˯0st`h{8x=HP]jƪ @T ]]tPZZPtpwGq\TQ\XQEȫ~˽䕀` #`W. e҅pAr `C$& |.3jQƑ11ˬMr `WGݛqj=3𥣁.: |I:Ns+xn͛X,fߔkn467ΉABpqE gUküuYRJqA縣l}xm1Rz6 Xָ\z!o$N9=)β/⌗OۺRmt 13YYy @[RG`ǦgL\2=(:m_#//jj uF״4o5=:7Zƅ^ ";08*xv1S>0 ZOj.-W@Fs[eIN-4<3˯/C|iy_'>{o?;3.>QəGA+$;㕴L9s3&psLQ|GqZY pԙ4?TDd B C S AA? 2i(X=&}%2 E/p`!=(X=&}%2 p 8 xKA߼޺{aaN?Z@ڤP O4DAN,%)R B@+Jᔄd33of s~k޼} 4 bQJ\,dLi&I4#OiƐi.4qW>+T  THӥ}x6BK_NG='uٓ9Oun+?+ )9Sfy1pGySrdʍ}>3@7n5zNrj"{!V76m햧IDdTB D S AB? 2c;88J8?2p`!7;88J8` PXJxcdd``~ @bD"L1JE `xX,56~) M @ k)+8 UXRYvo&`0L`A $37X/\!(?71A]<6zοCLl3`?~8lr2W&hrpenR~̅` .p( 5S'@+KRsޡD];DdpB E S AC? 2׾U* a!3p`!y׾U* a!F)GxkA߼]~۽"E ?RY[S'(dM0biB{"L+7xX#יy7PcfvTW_<*"!23 ,әy63 Lus] ;ޓh\F3Q S"/r]eiRkj{#8^IisIIEu5< ܻ StA=`+ͭ$AwYDdW B F S AD? 2|uY@xdcieX:7p`!PuY@xdcie88xOA߼;v` 1T$N MuB\$QXP\QCCjCL0`T\g;{ǎ2@e#: a,$1+₱qnm@.`]5Q}dS +H'Q/FLQA oQMSZ1mښvzBy6/B|Ԋ3ы3@@I'#Xbl@UrOx+b<== qT܅u/͓E" >x2Q!ގ3AtWWu HaThz\H 50Ԛ>BkP42Xsk-JL4CBrC%}Qk\%Qic/T-pAOQg=8 )Ikv[3Mr0Q4`ʓdM{\i& m5YYP|mdQg{mx2M{/@ #SGr92#VrHA\!Ҳ'5kC|fu,]V>qX4}(#H?f̞ , kY]]aar oHSajU:23(-0:+{B[aMŲߊPh~ҕ `aLfrFaSjz[*`HƣVVqeƱYܦ_Cu|TrOK~НIRY3ُ騌, Hd{HD Oh[TW k^gdQ$oR7B'cߡ>ALAT!>~DdTB  S A? 2c-`blmRS%??p`!7-`blmRS%` PXJxcdd``~ @bD"L1JE `xX,56~) M @ k)+8 UXRYvo&`0L`A $37X/\!(?71]<6zga!&6HDF?Mn` 3)`_! BI9 L0Bc v-4*LPPcdbR ,.IexFf:;CDd B  S A? 20Z~*Г/h Ap`!Z~*Г/h\`8xO/A߼mvqA7um&H N."i87n>D  Akl'aپ>6M#AF!1~!ԤIԌ! c،s\K8/|ɥ3~ 3&0\E,*B\b 9R7VSm,[_*>rq#9SNή+'*36qv a1ɩʥʐoWM[eWvRY;y I6f2.Hx"&-f߁o&s331u)7lM;伶f]hTwW' F#* Cra$:kJscg ~ \e$_t*S\\˙Ll#W~A bq [,:3*Dd B  S A? 2e&KզGĺ ADp`!9&KզGĺ `'8xKA߼So܇_a" X?@-?<уp`"XE +IK4יy).~>{ (y115}5L'2m~QjcBHotOo8a"& S<լ(z p;&̷l7gW22"EaP#]n k5z ;5ao]q86Ag!c.nۏJ2jw"1>N-< ֒>{ Rnj;b/vrCӕqյ+)UU $hv(hPϵmV=ۛ,g 9+׼5O\{+cO|akMHn3y-dA^>~i@Nu̔ځf͓b6ו5'Dd B  S A? 2y?1mȿUGp`!M?1mȿx xkSAggw{ă$EhO%^=޵ IڊcCz@gkP ?Z𹻳Y6P0̾A !ՌP[BMd̬0̲̬LfeUn)RŠ N(*뙚 z|&ח.[)8TƀƄ9(8Ci봲}u2fVݑW;Za1##f2DH5ӵAJsiEAip_ !8o}W|}B'+ y[ :7nq2ImsUR+JJ`^ziܞv+1y-؆˝<<ǵ؏CͫN"͜?"{r}}OV'G%vwI8g-?Oj><yZY~͈;@W?Ӓ'b onKC+Y _5 ?zߏz|ez 1Ы4q6gzڄFDdB  S A? 2p3z90V39LJp`!D3z90V39ݨ @Px xkAygnvI@$AH@(+"p i@:+N ZQB #;7^@q7< d ]9JBIKCa}Eۅ ۺmPj"QY[n6buk=Z23 }?R@U]uG-zR U~v.7k" {=>v"XeygX~+8<3r~揖s!7Wzxcnb?{g~gzO#Or WO_#ه}˷diKx.G~ZŸ~I`|C'0!3H 7W^ov^oDd B  S A? 2V֣5*a6Mp`!V֣5*a6 A({xkQ;G6_ R R@o 7RqAi5xP*zAwBP{PڐkoSa͛73ovxVICEB`EBr2clilnbcّ#[!@f;ES~_R^1]xX5oQkZ!9D&e]P|g4_LqXҾ7wtQۚy&;2In&Qkf|}ܓ1#<.VLcM{`e$i5-L5ĜLKzm*ro5-(ӅDd` B H S AF? 2 YBdp"‰Qp`!YBdp"‰@(+xAKQͮfK*D'uB:("KEAA_{uڱSAx(h{oia=f;3o`?  eL1ay팳! Sa  0x" nՈLXD`ZoM WfR=xi+ƭ@@IO1)UZrM.U+MC ߓ F \<9"89<<$8>rAŮ~E\7yO"+m e:2UMzN*-5%wK;c[lk΅l VMqLNvru*Gϒ#FNU)Mq %h6M֣%?PV3eϢjd\Im1T^q+A~_v%Dd pB I S AG?  2BߝU̟I< ,GrT仢bN1}>ws9w#m +0J2 Jf]DW9I/'U]FmZ~ƈ5{%_ܔ3?smue® M65⇫UYMn;nU.5rO#O∩rT#|##9/<s;USAbcފpx:tvDd pB J S AH? !2GH'a&֞\~#Vp`!H'a&֞\~H`xKA{3kۋwꉚB Ie8MbMVh ;!^w""6 Λ (evgx7｝AH^<<5SĖT REzaBӭ.Cu}ge D,↲ :Fo}2090S[  rk2 z!4Ԡg[Yդ_zrӵ\#"HckE=MhWۙ>c7|hySt0_Xmui>wwi}O4|,h9M X_A|(m9*f?6&N]',ˢ?z+Ẉ!K4 7Sz]BPVhc5\,ϪXU˴-bT+Y>.K(x}}\qƏs ɸ "E`i}Suܪo.kե' wArvDdP L S AJ? ""2ԔOc5~Yp`!ԔOc5~  8>L txcdd``nc ĜL  312Ec21BUs301)p Yjl R A@?Jjx|K2B* RnaJ`u!010`\ UBN9 +ss z8Wk;3H'(5~sn7/Hi$_ɂx <_ wdA,@C2sSRs`> nAP 36p"?a@? {]B])d = XMւ-|Q0'-`$.pjQP= ϿcdbR ,.IexZf:& pDd sB  S A? #2s?ϊFWh+\p`!s?ϊFWh@`PxR=KA;^b?BDF =llI&BXXY)D,`eΝٻût;;ｽA0P`xtKj y'+38*+s~vs)6M$20*dH2I?'ZiY >c\sQFLUԝ`tsP4d]X׊Gz-*=;o]B%7|&'NG#g2`V`{U@5TV`|Y|llޏ{?j& =L%V/oebU^*:z·^GoБ[-ߎ3'pwAvGOINͅx:ċ K!NgŅ6~h|~,-wit4-W 7ZхVܓ!y?zzDd@B  S A? $2`2bve iR8.<^p`!42bve iR8. xcdd`` @bD"L1JE `x Yjl R A@Q N*; UXRYvo`0L`A $37X/\!(?71]<6J`\Rl糀&20H&3 4} \sD?#\?N[ Xc b\P LPP R 盂}mM.pj(}PyĤ\Y\`u`;,Dd`P M S AK? "&2V{.[zKV:dbp`!\V{.[zKV:j$X *xڝo@߽sq& $t@DKeUAX*RM! LX`bH e` #  ܻ_[s}|w r|,(=Z10cs='iuq.VeJE81'xK6U6l5.r{#1vE,gVx%ԚMoL#:AT0=2@r9gюr$fbpcu!#{k_?K:YP5؛2$#>pIcFP%4Z|pva5l]Ư++wB)g<:ΤӼΖˣh.yTO*g:Lz\v>|`]s\_㍬9VVzs5c\Fm'$sR k EǗqR4Fǯsc*ow:Nkv_fXGSЮJ? "; qv Bvť''/DdB  S A? '2Ky60([Χ*'fp`!y60([Χ*j@Rxcdd`` @bD"L1JE `xX,56~) M @ jh+P#7T obIFHeA*Xo`0L`;A 27)? d.PHq)0~a)( Мbr<f`}@2ن N._A\) 9 ;F&&\w0WBdd`327Dd@B  S A? (2kDpz|TŌ?2A0%Ggp`!?Dpz|TŌ?2A0%   xAJAE$b& ,tI\x ]\` N@f'xMN,>66лk XS\dI̭^Y].Sdu? PDd<B  S A? )2zo[Pip`!zo[P@`` PxR=KA|F"HXF!Ia<#^@S . v"XXZl๳w3 ޼}7 LzLqH!2&3 =ϓedG.u$d"H э8V #d⚓rݬuvmg>PUГLiϞf_* fΆب炣^?|C[ r~DTޗ>f?dm˱]k޷*-p9#8|e׸O E~ g,7Y8m@א~8Fv$9`zF(~I`R#ȡrZ=h57!1l% 1}1gNbq۶t\qnr{DdB  S A? *2GZ7T-5 Vylp`!GZ7T-5 V0 L xRJAHP0ډ"IDYL8|jWqc6\_}c)GvSX5NrL|WR6ZijFco4#(5Tx:}H!M0^*oڣ:i}QrT*h';9Eֳcw|U}$ʕ͖@t}QsDdpB  S A? +2Ӥ'3#@np`!Ӥ'3#@P L xRJA1wI0hIpBtB.D.Ie^@$`!bX,\w=voo曝] @B ait6 Qx0%eBNS!0)f͛PAf  58jv`Y-J2G(.̞'d9{!j=o} $cR_}chpJ%UVy>~C8ߣdr'j1k_}NqG)mݶl\G'J(?j,bXHg8TIZ(xuGu?roS/vr?%r)W_d&G/ ›x7$"Ilh+իȋ!Suk uxeDd$ (B  S A? ,2H/=.o0SX:xqp`!H/=.o0SX:qxKP.ImXVAt`d\[(+"D7'A'N 7AA/̫n5ǚ Y~Ev2W=;9]<#$~(C~aDd B  S A? -2Rz{8l{݁6.sp`!&z{8l{݁6xKA߼ٕd6Q(=E,$,,br.h֖ *؀?K<CVċzK{hՂT7o2yD@@N^U#9jzF`zxg(LvuIlLRBAZqCE[jgިԄIBV | W&zeUIQV ׯ8-՝.SςWw~)2#/e<2zcr"E|fxs/|d? Nxа/Ţ\cz|GZz[r/l<`F+NisS \IJh*}u. [x\p󖯠͑qfp!V-ƭ.cOS˟.{0*z'm:z\麫ED;iF~<{kgv K bmi9(igR$M/9DdhB   S A ? .2[9̕{kGvp`!w[9̕{kG @ |Excdd``.gd``beV dX,XĐ ɁICRcgb v@P5< %! `~}vL@(\_(j-n&R#B7cga/D?#TcH ~o`le)Ն9A63o&H1 M-VK-WMc`e4 1d5+&`Hn,2m |.hZ'!.J@121)W2Cw=3X7o8DdhB ! S A!? /26;ZCx~xp`!v6;ZCx @ |Dxcdd``.gd``beV dX,XĐ ɁICRcgb v@P5< %! `~} vL@(\_(-n&R#Ƃ}I?B? PHfnj_jBP~nbC&=`d K1&Pk24`Hn,2m |L?, )q"~L4p8vR/wLLJ% VqADdlTB " S A"? 02gupЩd~"C6{p`!;upЩd~" XJ xcdd`` @bD"L1JE `x0 Yjl R A@R ^p7$# !7S?C&:A 27)? d.PHq50N!CV}`@? d6翙#g`M-VK-WMc`Xs$FI724@MB^0d6 B\P; OPPcdbR ,.Iex:f:>JDd 4B # S A#? 124SH7t=V3}p`!SH7t=V px;KAgg/1E4( Ze$mڦ;-DV*ݝsݜc7 PܠEiYb"cjyjeu42Ư8:D OARb%nELPreސ"QeOָڄuzq#C4#$rnޙuw\v`0g&vm <1n5y]6SEh"*O2NȠAg͒Ӛ&gq7fx-"9s' ;x،/[7!qی;c%uZyYuj|Ee4Dr=u\Equation Native _1017040267AF ,,uation Equation.39q׌kIvI Ed"I p +I ka +I kb +I kc I n FMicrosoft Equation 3.0 DS Equation Equation.39qOle CompObj@BfObjInfoCEquation Native I8mI I n =23C 1 d 10" +"  2 d 2 d( 12 ""  102 +" 0" +" "  2 + 22 ) 02 ( 1 , 2 ,|"  1 ""  2 |) FMicrosoft Equation 3.0 DS Equation Equation.39q$vIpI I p =2C 1 d 1 V( 10" +" ) 2 d_1017040774?SFF,,Ole CompObjEGfObjInfoHEquation Native _1017041395:bKF`$,`$,Ole CompObjJLf 2 d( 12 ""  102 +" 0" +" "  2 + 22 ) 02 ( 1 , 2 ,|"  1 ""  2 |) FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoMEquation Native t_1017041832X]PF+, E,Ole XqII I ka ="2C! 2 m 1 d 10" +" 2f( 1 )f( 1 )+14 12 () 2 d 20" +" "CompObjOQfObjInfoREquation Native 8_1017041303UF E, E,   #$%&'()*-0369>CHLMNOPQRTUVWXZ FMicrosoft Equation 3.0 DS Equation Equation.39qDI8mI d( 12 ""  102 +" "  2 + 22 ) 02 ( 1 , 2 ,|"  1 ""  2 |)Ole CompObjTV fObjInfoW Equation Native   FMicrosoft Equation 3.0 DS Equation Equation.39qII I kb ="2C! 2 m 1 d 10" +" 2f( 1 )f( 1 )"12 1 () 2 d 20" +" 2f( 2 )f( 2 )"12 2 ()" FMicrosoft Equation 3.0 DS Equation Equation.39q_1017041474ZFiV,iV,Ole CompObjY[fObjInfo\Equation Native H_1017041853_F ^, ^,Ole CompObj^`f,tII dcos( 12 ""  102 +" "  2 + 22 ) 02 ( 1 , 2 ,|"  1 ""  2 |) FMicrosoft Equation 3.0 DS Equation Equation.39q$vIpI I kc ="3C! 2 m 12 d 10" +" 2f( 1 )f( 1 )"12 1 () 2 d 20" +" d 0ObjInfoa!Equation Native "_1017042020NdF ^, ^,Ole +2 +"  02 ( 1 , 2 ,|"  1 ""  2 |) FMicrosoft Equation 3.0 DS Equation Equation.39qTkIvI "  1 =2rCompObjce,fObjInfof.Equation Native /p_1017042097iF1g,1g,  1 "2r  2 FMicrosoft Equation 3.0 DS Equation Equation.39qTlI$I "  2 =2r  1 "2r  3EOle 1CompObjhj2fObjInfok4Equation Native 5p_1017042149gvnF1g,,Ole 7CompObjmo8fObjInfop: FMicrosoft Equation 3.0 DS Equation Equation.39q II "  1 FMicrosoft Equation 3.0 DS Equation Equation.39qEquation Native ;<_1017042172sF,,Ole <CompObjrt=fObjInfou?Equation Native @<_1017042251q{xF,,Ole A ,IDI "  2 FMicrosoft Equation 3.0 DS Equation Equation.39q$kIvI < 1 > FMicrosoft Equation 3.0 DS EqCompObjwyBfObjInfozDEquation Native E@_1017042649}F-,-,Ole FCompObj|~GfObjInfoIEquation Native J<uation Equation.39q IlI  1 Oh+'0 ( D P \ ht|,Variational study of fermionic helium dimerari PMF Splitl MF Normali B $ S A$? 22TļjW)l:KtR0p`!(ļjW)l:KtRxMKA{Vwgc@LAAԛ' 31 K.@<.Aweo!Ih tu| {~z}i"TGy3p~efVӦsNNm=mFv֟qJ wDaK B8nAL;FW{.{R6⮆*Ddx`P N S AL? "32?cd76 HQkbp`!Z?cd76 HQkz^&X (xڝkSAgf_%5ϼO1QDy/"BHE$Ps{IO (MPPMb|v;3;]4xELrIY3HQ),iBPo]`ldC'yCZ9@')Mkjv` e-]FKJ$9ezހ:HCZP] vMO-++7Z3n5V_iq ?ZxM烫O ^h6uS]:0;JdB|u sK=l@=߿)G/8,.WW-pN_$siNb3^D.rFpgdGc~ʙ=r_K|dmtmwӶl'5CFg8RC2BF\)6L\S|d[ΰ)@)CwmQ=#|Xj~w^5 y\~`LU\?]$*-z~Wj!DdhB % S A%? 428GŅO'68!_gp`!_8GŅO'68!_T @|-xcdd``bd``beV dX,XĐ Ɂ A?d-\ Ojx|K2B* R. XB2sSRsA.Jsi#\ p?_ fEofXansGMp~) /i2 W&00|1? οᣛǀFE|Fo8#A2p`!FE|Fo8#Ax x$dx/A߼9;?( $ ??G.{.$@hh4(=:T*55ofor$l2y?vfD#4I C5KK/@ǒ_ӑz1k l]4qh0-7sϔ |UFbjN͒ǣVIY%ֆRҌlqe< "^ũC0%{f㹭Ԇ]W❱|l$q8q{"$jITYwpTrfϠ*pw]>L<HGp65~ZPoU颻Xʇ:?8iSOy\6j=O?ԑKnxXrDqK?ϒYN>;<|Jg 75/Xn%o<Kt(Uq׳z;#v_ԡ|`{)tGamn`ǬVo7$~xq7Gl-nkwxQ/Yݑ=vừƕDٕ#<"8h~lU^h=_NzӜ?QR`z@8 5H`@P| xcdd``~ @bD"L1JE `xX,56~) M @ k)+x UXRYvo`0L`A $37X/\!(?71]<6j`\ R /f5&2HDF?M~69Wf BI9 L0BcnIp .pCG@+KRsޡESSDd B ) S A)? 82~ѽ@kz5O%pp`!~ѽ@kz5O%p8`h_xJA9 $b!Z$􂕝&]"pllE'QV3AGAefs F%VP%U'DAJTf,3ML.1uˋjZ,C R6ݨ64Fǝ,Jo$W(YT:8{y?{Τoy!MXix;`nMÏ&_%Һa^-ϤJ;'@ ?4%놟[_Hzݮ ]٥6;G}Jykb#sH9l!3/#5eΓ)Ũ;P Vp0kȉ%sUDdt B * S A*? 92'huz07Xp`!'huz078 qhaxJAg&|"$h5mJ¤ hS*leC5RD͠{Ꝇ A,% r( ;Vxo37<,^1Ly5n.:bQDDZ4: U[I}f/k+دXcxc0~w]ۜjO7vu>{1~{=;0\^rgu|/L>S^+BE 3Yqh|7uq4ggݩ bi;Isk/0Ή޹{(g<2M9GoDܤ @t+M-:g̫E_6;GNEWhlQߨp_ԺDdPB + S A+? ;2b~ZVb^ƧԦW>p`!6~ZVb^ƧԦW %dxKAƿyMQ <"Zz xbՋX`4A{Tz?PJ$ ' ^ܣFZiiجda:I=Ӗ2߷\b|;L>Sv+@u%G,~LxŎk*O_ٵgT>/ZcU3f}*%:|bc6-;Q$ oM+{It:t,+p D[@?۲ly}W/lv]jeXE|R>] Dd B . S A.? <2sraQajp MOp`!GraQajp M8xT1kA~eow]b" p-,H@@!&M ^d7 &*WA0Kb"a ],lN Ҁy;*p7{̾X àWEHMAʲ0p0: {.M U#h@ApOEj"IU&5!\[ܸ3]k+^ ƌECT\::EHnԘ+ t+5^lU怞 s+bs=(szOf=9zXǁLB=C5,{~mHsAd=U' {}fN^o^o?lXMW~[/zZ"|V1=tpP73P8*:HPo |?j>=rgϻD^iGܮ3 G%|t\gjnn z~ҟOp ޱgjE70UIx|or! ?!v7)H LwDdB / S A/? =20hhgԴq=5ݹ p`!hhgԴq=5ݹ>` `/dxK@߽Pkm_Av:(TA\R`TlA . {'ͥ\Dx hʥsw1hco||"dL0,K̰I#sCօG<@,*;a2R­/bphm dp`!R­/bphm `G^xKP.鏤!V(NKQѿ@D:PjB?XptpYX n w8{qw,%Q"L Q.G]UmWnc;'Ob~[1Yf̏@+W{W-9/pIq&͟4#}2ouρh=[.ph5\YэhV$SxNRχߞ =ZqDdlB 1 S A1? ?28-'j59z@p`!8-'j59z@+بB}xkA&iIIm*[[֊MAPPD`<؀(`ژƏ^TMы^B<`,(RqL2hۅI7cޛy3 ` =_ǞO4Θahȑ,!G8kjy.W @F` +Md+j t0?[8ʔ8؋^ԇw(L]-ӧ ҧY Ϙ!ל?ۋ5-?$yfӦyXsq7y!/' &P@cpk:::SCc-NSyRA-ʗ< FtE)-s+A4T(BSt(<#FEM5U-^U1jپa/k>:Hy٦ýq 5a7[wz%=ͥ߮[v 3HS^wtƭ#ռ!YR#c;: L|}wY_4/wQWݑg7=l{oGv(\_=T_n7>wۛE+'Zz_LFǣ4տ4_0׃6bX$*əI@$>ʫ|Ag[^;@9S>D3`[&,4~+{$4_.)dt$)')/wXdNM+>@PN:CvsvO;%"~'L!fo7ѝ˳dP5}Tߔ]߮ ]q7* }]#k=mx ^ 5ƹ9V+PFyۘ@lDd B  S A? A2.;G#f8p`!.;G#f8@_,8xxMhSAgg_j~MkX(b!=Z6 FZjI#&"C"ɃzB%zPQ4nmuþ7;7aI..1=H+KLdLJv:)9RB}ص#'buh !# 51/'քL2 =&ro,hȈLyhi+ yK?6OhVȕ {pT^k燈h~N^)l??{'X?{M>c߲`xvn#NT!1p`!)8TJ>T! *kxK[Ag%1ie@ RDQߥPs 4@ ?!@A1;2{5 b: *s>yG3d}6V`v+P̾ج<2'I?tNmvgzRlN*,ki?wwI_]xwLz#{;=K訋s? k$^*Uv3"~DdB  S A? C26/_yz U3p`! /_yz U3&:`\xMhAglcL&1mM?VmAoBQD4To4R4Z(ģBAIaB/E */EH*;ٗh6ߛ; %>B2_$NUooTZ(eiA'.A:&ͤ,H=gm2eO fÅYB~WJfJ='`#FQ>j:ٍeıGøcL:˦c+8km"*Ror Z(>ۅm<ӆ6?ft<洡W^c:E]aN+).Ü6WS\:ς[=oa{ݗk^3Ʈo_4*Vz^Wp՜) etyd29CȽ?WzXhA}} {!+e4Mkz^ w+/tϛ6z|}|ϸ |M3XQ>/=e"-Ez͗H7ǰ~4WCX?y ү/gKLwJsrb 7aI1̷Xo!'Wwwg%EIb 1;!?9=R'x"xm]o%=2'"Hn48ld^?Q_uwNLz*RPPa:͑ꪘ T.Dd80B K S AI? D2bP9S}|blh>p`!6P9S}|blh"p/kxK[AgE/Tz(UTzh]ZOz 5` ɟz/= ^*=GoξSggwgv!`A Fx mre;z\QooAlSXq}0--fʫ9TpC{)Q 03K\15HM-V2(A?谇ETe`O\_m}[{OqV(~fYTkFM0(cq}cmyX7M>f/x^N?GσUL_ @:@]89Vvb:/Eu |ڤsyMq {*<7e"}.#*G+^T) ɮnU ⓐw;#KްG%䫴apޗ|dSeqDR.~u{hDdlB 3 S A3? E2LCشpNHdTS(p`! CشpNHdTS+0D`\xKTAg\uZmSg="JX/BCK=VD F+叶q0s̻ܻ9g̙=w":TU@"`-ހ1`rrWqK`bH[PXjP!r^Y BctݧEfbQ6 m`W؆A UN[;6_[cб=dچŘ1_ sZ<:mGoZ'a659I=Vɿ:g,ƍ6g N1T02MWJ4n 46M՟KHb:˕[dI"cj]#a.K{9ۜ?I>RIR" U5pʭpO$yo>SuGMWmQ+П90GTq}$7<TGtݐFǪTΐP S4~m:o 6])|'QY2f"Rl [bxq,}e/$?x!diйE,_Mo^|j~"K}ݎ{{\_ɐ]^؟ |W [^ݚYޭV7Qk*gH-WSȯ_~=qOޮw5Λ+>$NG?Amd5>Y Q֭g6Dd8TB 4 S A4? F2 r_?Fle|p`!t r_?Fle v XJBxRJ@}iCEA<*wA*j J% {_x w8m n2ov۝%MȪՕx6E#,ӑ=ґ"PE]Syjf۵װL27eKm &^_mj_ *\* GIxx%mޯ|P͖n'N=q!.:?HkUj%>r,'=;#9g$0go']с?DYCER%n/JE)=笇e87Uz1'v(#5Z:c[D8DdLhB 5 S A5? G2ռ0|~F%TM;I~żp`!vռ0|~F%TM;I@ |Dxcdd``vfd``beV dX,XĐ Ɂ A?d-l Ojx|K2B* R. `W01d++&10,D(0걁ǙA|C8ߌ7f#~q/+HO <ɾ! %E@&0C1 `+ss`cx H.o 9[ FO{qgpdA* J+KRsޡIj]oDd,TB 6 S A6? H2dS5| =aނ@p`!8S5| =aނ샜 XJx]PJA}3\& t ,,"bN80K$9ץ iB,ll|AHp,20켷 T0Nq Yg%:tfSnpk5Kխ )՛䫀$a~?S ܙÛ`am:w,B弊H{׎?%1adÑ9tO TA?v4)(0 Qp{T%>t_b><ͰWU_{>hDd@TB 7 S A7? I2d=uý%?a@p`!8=uý%?a  XJx]P1jQ}3F$Ւ.B,E C{ ,Ơ q is oaa6g ^wf7ß? 0.QV'%s:]j[O׸9dTJp BSV}IL8Gkܛ=Ù|`44w[0I`JT^C}o@jLFy8yȜKhu`y6 x x w{U%ֺ-1_Y*=DdTB 8 S A8? J2[Y>KU7p`!/Y>KU@ XJxcdd`` @bD"L1JE `xX,56~) M @ k)Ԉ@P5< %! `0,&ܤ&@Q mh Rb16`fbd Мbr<f`};C 1pD?#% E \Pr"={Ĥ\Y\M`u=DdTB 9 S A9? K2W4Kk# 34`3p`!+4Kk# 34` @CXJxmjAMSH+-m$  bPAG%ė|\gdaٹ% ]wUVD!vYN4!Q<)|NE5E'7:pf32R+{4 ?qXl[:`2ă7̑%_Əʷ6+|җK7O[OӝZU>DdTB : S A8? L2[Y>KU7p`!/Y>KU@ XJxcdd`` @bD"L1JE `xX,56~) M @ k)Ԉ@P5< %! `0,&ܤ&@Q mh Rb16`fbd Мbr<f`};C 1pD?#% E \Pr"={Ĥ\Y\M`u=DdTB ; S A9? M2W4Kk# 34`3p`!+4Kk# 34` @CXJxmjAMSH+-m$  bPAG%ė|\gdaٹ% ]wUVD!vYN4!Q<)|NE5E'7:pf32R+{4 ?qXl[:`2ă7̑%_Əʷ6+|җK7O[OӝZU>1Table 2SummaryInformation(KDocumentSummaryInformation8SLCompObjYjPMF Splitl 26 Microsoft Word 9.0f@(@*@jܣ@4 8 ՜.+,0 hp   PMF SplitawD ,Variational study of fermionic helium dimer Title  FMicrosoft Word Document MSWordDocWord.Document.89q i0@0 Normal_HmH sH tH <A@< Default Paragraph Font, @, Footer  9r LOL jednad~ba  uB*CJhmHsHtH uTOT jednad~ba2$ ]a$B*CJhmHsHtH u6O"6 jednad~ba1 z&)@1& Page NumberDD.KLM} 3 4 5 ] ^ J|Qo$Cb2Qp *opq-. :;z8<[ "Y"I#h##$$&&&E&F&G&(())***!+&+?+C+b++,,--..<.Y.q.....:1;1<1=1>1?1O1P1Q125H89:::;;;;;;;;;;0<F<G<<<<<<>=?=====5>6>y>z>>>??J?K?????@@Z@[@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@'A0AAAAAAAAAAAAAABBBBBBBBBBBBTBUBkBlBCCCCCCCD D D DDDDD0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000@000000000000000000@0@0@0@0@0@0 000 yK#\!"#&',)-9/z0P33u4;AFMCGIJKLMNOQRSTUVXYZ[\^_`ace%1@EVGdIjMMDFHPW]bdfghME-/2FHK_adxz}7KMRfhp%9;DXZ')3GIRfhq  "#%.BD-ACn.0=QS"""$"8":""""" # #J#^#`#i#}##$$$((()))))) **!****+++'+;+=+D+X+Z+c+w+y+,,,- . ..1.3.<.P.R.Y.m.o.r............. / //%/'/D/X/Z/`/t/v/01 11-1/1 66 6/6C6E6D:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: !!  ?"$ DH2Iļ/"c%_"$6Rka{DME%_"$\)ێtY%)z+%_@ |(  D    A"B S  ?@D d$t-.JM|} d#g###**+ +!+%+....8.;.U.X...<<<<<<<<<<BBBSBUBjBlBCC DDD-.JM|} a#g###$$* +!+%+....4.;.S.X...<<<<====(=(=4=<=>>@@@@@@@!A"A&ABBBSBUBjBlBCC DDDY_$$*'+-Y.r..#=?=>>!A0ACCC DDD PMF SplitC:\My Documents\kv2003.doc PMF SplitC:\My Documents\kv2003.doc PMF Split/C:\WINDOWS\TEMP\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asd PMF SplitJC:\WINDOWS\Application Data\Microsoft\Word\AutoRecovery save of kv2003.asdCC DDD@::Lw::LK<K=KAKBDpp @pBp@pHpJUnknownG:Times New Roman5Symbol3& :Arial"h\DF&G& G&# 8w!0dD2+Variational study of fermionic helium dimer PMF Split PMF Split