Velocity-dependent transverse momentum distribution of projectilelike fragments at 95 MeV/u. Sadao MOMOTA Kochi University of Technology

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1 5th International Conference on Nuclear ragmentation Oct./-/5, Kemer, Turkey Velocity-dependent transverse momentum distribution of projectilelike fragments at 95 MeV/u Sadao MOMOTA Kochi University of Technology r8n collaboration Introduction

2 Investigation of unstable nuclei Inverse kinematics scheme vp Nucleus of interests IE, Transfer, Exchange, Preparation of radioactive nuclear beams (RNBs) ) Wide range in nuclear chart ) High quality as a beam S. Momota NURA5, Oct./9/5 ragmentation process A Z Participant-spectator picture pre fragment vp v Satisfies two requirements ) High productivity for wide range of isotopes ) High beam quality Usually applied at RNB facilities S. Momota NURA5, Oct./9/5

3 Production of a wide range of isotopes ragments prod. from Sn+ Sn at AGeV V. öhr et al., Phys. Rev. C 8, 55 (). Produced isotopes Sn AGeV Sn 5 S. Momota NURA5, Oct./9/5 High quality as secondary beam Momentum distribution of fragments E dissipation : low rrow width Simple & well studied at relativistic E PL distribution of Be produced from C (. GeV/nucleon)+ 9 Be D.E. Greiner et al., Phys. Rev. Lett. 5(975) 5 Low E dissipation rrow width Therefore Separation of objective isotope with high efficiency P=88 MeV/c/A S. Momota NURA5, Oct./9/5

ormulation for practical use Transportation/separation of fragments through fragment separator Performance of separator is simulated by means of LISE++, MOCADI, Ex.

Momota NURA5, Oct./9/5 Object of this talk Remarkable and systematic correlation between PT distribution and PL of fragmentation products at E~ MeV/u.

4 ormulation for practical use Transportation/separation of fragments through fragment separator Performance of separator is simulated by means of LISE++, MOCADI, Ex. Ca(8 AMeV) + Be optimized for LISE++ Key parameters for simulation!prod. PL, PT distribution ew systematic studies on PT 7 S. Momota NURA5, Oct./9/5 Object of this talk Remarkable and systematic correlation between PT distribution and PL of fragmentation products at E~ MeV/u. Earlier works on PL, PT distributions. Experimental (RIPS-RIKEN). Correlation obtained from experimental results. Comparison with microscopic dynamic model 5. Conclusions 8 S. Momota NURA5, Oct./9/5

5 Previous studies on momentum distributions 9 Isotropic distribution at relativistic E E GeV/u PL distribution of Be Ca(. GeV/nucleon)+ 9 Be D.E. Greiner et al., Phys. Rev. Lett. 5(975) 5 Low E dissipation rrow width Gaussian-type distribution with small energy dissipation Isotropic distribution!l =!T to an accuracy of % Contribution of ermi momentum S. Momota NURA5, Oct./9/5

6 Model based on ermi momentum Assumption : Independent removal of nucleons in projectile Momentum distribution of fragments corresponds to statistical sum of ermi momentum for each removed nucleon. ormulation proposed by Goldhaber σ GH = A (A P A ) σ A P P P : ermi momentum of nucleon in projectile σ = P 5 ~ MeV/c A.s. Goldhaber, Phys. Lett. B 5, (97). Simple and successfully applied to a wide range of reaction system Success of Goldhaber model Width of PL distribution of fragments Ar(.5 GeV/nucleon)+ 9 Be M. Caamano et al., Nucl. Phys. A 7() 87. σ = 98. MeV/c P 5 ~ MeV/c

7 Deviation from isotropic dist. at E ~ MeV/u PL distribution : Low momentum tail PL distribution at 9 MeV/u Ar + 9 Be + X Universal parametrization obtained from experimental results O. Tarasov, Nucl. Phys. A 7 () 5. f (P L ) = exp P L P τ erf L P +σ pf /τ s τ σ pf τ = coef A E S β σ pf = βσ pf A (A P A ) A P ormulated momentum distributions have been incorporated into simulation. M. Notani et al., Phys. Rev. C 7 (7) 5. S. Momota NURA5, Oct./9/5 Deviation from isotropic dist. at E ~ MeV/u PT distribution : Additional width PT distribution observed at 9 MeV/u O + 7 Al A Z + X K van Bibber et al., Phys. Rev. Lett. (979) 8. Additional width due to orbital deflection by target nucleus σ T = σ GH +σ D Empirical formulation for σd σ D = A (A ) A P (A P ) σ Usually applied with " ~ MeV/c. However, the reliability of the formulation is doubtful scarce systematic measurements at E ~ MeV/u no measurements as a func. of v. suggested from asymmetric Pl dist. S. Momota NURA5, Oct./9/5

8 Velocity dependent PT distribution Angular dist. observed at MeV/u Ar + 58 Ni + X Expected trend for width of PT distribution v >.5 c v <.5 c Contribution of collective effect was considered to understand v-dep. angular distribution. Width of distribution Velocity V. Borrel et al., Z. Phys. A (98) 9. It is suggestive, but further investigations are needed to ) formulate v-dependent behavior ) understand based on reaction process. 5 S. Momota NURA5, Oct./9/5 Experimental

9 Experimental : fragment separator RIKEN Ring cyclotron + RIPS Reaction : Ar (95 MeV/u) + 9 Be Current monitor Target D Swinger mag. D () 7 S. Momota NURA5, Oct./9/5 Experimental : fragment separator RIKEN Ring cyclotron + RIPS Reaction : Ar (95 MeV/u) + 9 Be Current monitor Target D Identification : TO, #E, B$ Swinger mag. TO, #E, B$ A, Z, v D () 8 S. Momota NURA5, Oct./9/5

10 Experimental : fragment separator RIKEN Ring cyclotron + RIPS Reaction : Ar (95 MeV/u) + 9 Be Current monitor Target D Identification : TO, #E, B$ Swinger mag. Acceptance : Slit after target, #P/P = ±.5 % #θx, #θy = ± 7.5 mrad () 9 S. Momota NURA5, Oct./9/5 Experimental : fragment separator RIKEN Ring cyclotron + RIPS Reaction : Ar (95 MeV/u) + 9 Be Current monitor Target D Identification : TO, #E, B$ Swinger mag. Acceptance : Slit after target, Beam intensity monitor : PL@target Ambiguity of beam intensity : ~ ± 5 % S. Momota NURA5, Oct./9/5

11 Experimental : fragment separator RIKEN Ring cyclotron + RIPS Reaction : Ar (95 MeV/u) + 9 Be Current monitor Swinger mag. Target D Identification : TO, #E, B$ Acceptance : Slit after target, D Beam intensity monitor : PL@target Ambiguity of beam intensity : ~ ± 5 % Angular distribution : Beam swinger + slit after target () Keep optical axis of RIPS at any angle setting Constant values for transmission and detection efficiencies of fragmentation products. S. Momota NURA5, Oct./9/5 Results & Analysis

12 Width of PT distribution Obtained from angular distribution Prod. rate /( Ar Acpt.) Prod. rate /( Ar Acpt.) Prod. rate /( Ar Acpt.) Angle (mrad) Angle (mrad) Angle (mrad) B$ =. Tm Be O Prod. rate /( Ar Acpt.) Prod. rate /( Ar Acpt.) Prod. rate /( Ar Acpt.) A = A = 5 A = A = 5 Angle (mrad) Angle (mrad) Angle (mrad) C 5 A = 5 5 Al A = 5 itting with a Gaussian function N(θ) = Aexp θ σ θ with considering ) inite angular acceptance ± 7.5 mrad ) Angular struggling in target evaluated by ATIMA ) Emittance of primary beam assumed to be neglected Width of PT distribution!t = PL!% S. Momota et al., Phys. Rev. C 9, 8 (5). S. Momota NURA5, Oct./9/5 Correlation between "T and velocity Ar + Be + X - 5x - (a) Prod. rate /( Ar Acpt.) 5 (b) 5.. P L (MeV/c) GH + Bibber GH.x S. Momota et al., Phys. Rev. C 9, 8 (5). &P : shift from primary beam velocity PL distribution Deceleration : ~ MeV/c Larger width for low PL Remarkable decreasing trend Agreement with reference values GH@primary beam velocity GH+Bibber@center of PL dist. S. Momota NURA5, Oct./9/5

13 Correlation between "T and &PL A = ~ Universal behaviors of "T A = ~ A = A = A = A = A = A = A = A = 5 Be Be B Be B B C O O O A = A = 5 A = A = 7 A = A = 7 A = 8 A = 9 B C N B C N C N C N O Al Al A = 8 A = 9 A = A = A = A = A = A = N C N N O N O O Al Al Al Al O Si Si Si Si itting by a linear function : "T = k + k &PL 5 S. Momota NURA5, Oct./9/5 "T at projectile velocity : k Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) x P L (MeV/c) k (MeV/c) GH GH + Bibber B, C N, O,, Al, Si A Good agreement with Goldhaber formulation No additional dispersions are not needed. S. Momota NURA5, Oct./9/5

14 Reduced width : " Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - σ GH = A (A P A ) σ A P 5...x P L (MeV/c) σ (MeV/c) 8 A Av. = 9. ±. MeV/c 9.5 ±. MeV/c obtained from PL dist., Ar(9 MeV/u) + Be M. Notani et al., Phys. Rev. C 7 (7) 5. Good agreement with " obtained from PL dist. 7 S. Momota NURA5, Oct./9/5 "T at center of PL distribution Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - In order to compare with the previous results, most probable "T, <"T>, is introduced. <"T> : "T at center of PL distribution 5...x P L (MeV/c) "T at E=9.5 MeV/u O + Au <σ T > (MeV/c) GH GH + Bibber A K van Bibber et al., Phys. Rev. Lett. (979) 8. Consistent with previous results on "T 8 S. Momota NURA5, Oct./9/5

15 Slope parameter : k Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - Parabolic behavior of k x P L (MeV/c) Parameter to characterize decreasing trend k A itting by a quadratic function : k = A +.A 9 S. Momota NURA5, Oct./9/5 Empirical formulation of "T Width of PT distribution : "T Monotonically decreasing with velocity "T = k + k &PL "T at projectile velocity : k "T(&PL=) = "L = "GH Slope parameter : k Depends on A k = A +.A Microscopic reaction model can reproduce behaviors of "T? can reveal origin of the behaviors? S. Momota NURA5, Oct./9/5

Microscopic reaction model Collective features -> Additional dispersion and deceleration effect Abrasion, Excitation AMD Ar(87. MeV/A)+ 9 Be b = ~ fm Gogny type int. A. Ono, Phys. Rev. C 59, 85 (999).

16 Microscopic reaction model Collective features -> Additional dispersion and deceleration effect Abrasion, Excitation AMD Ar(87. MeV/A)+ 9 Be b = ~ fm Gogny type int. A. Ono, Phys. Rev. C 59, 85 (999). Evaporation Statistical decay T. Maruyama et al., Prog. Theor. Phys. 87, 7 (99). S. Momota NURA5, Oct./9/5 PT distribution obtained by simulation Ar + Be 5 + X Prod. Rate (normalized at P T = 78 MeV/c) AMD GHAMD GH + Bibber P T (MeV/c) 5 8 PT distribution obtained from AMD + SD calculation Gaussian-like distribution Width is consistent with conventional values itting with a Gaussian function as for experimental results "T(AMD) S. Momota NURA5, Oct./9/5

17 Correlation between "T and &PL A = ~ A = ~ A = A = A = A = A = A = A = A = 5 B B C C C Al A = A = 5 A = A = 7 A = A = 7 A = 8 A = 9 N N O O Al Al Al Remarkable Al agreement Si for Si A = ~ Si P A = 8 A = 9 A = A = A = A = A = A = Si P Si P S AMD calculation roughly reproduces behaviors of "T. itting with a linear function k, k Si P S P S Cl "T at projectile velocity : k Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - 5 AMD+SD...x P L (MeV/c) k (MeV/c) GH GH + Bibber B, C N, O,, Al, Si A Not so bad, but systematically underestimate k at A >.

Slope parameter : k Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - Parabolic trend of k obtained from experimental results. 5.5....x P L (MeV/c) k -.5 -.

18 Slope parameter : k Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) - Parabolic trend of k obtained from experimental results x P L (MeV/c) k A AMD calculation roughly reproduces negative values for k. Large scattering prevents further investigations on k. 5 b-dependent PL distribution Impact parameter Collective/dissipative nature Therefore, PL distribution is expected to depends on impact parameter. Calculated PL distribution b Prod. rate of Si vs. b Δσ/Δb (mb/fm) b (fm) r ( Ar) + r ( 9 Be) =. fm r = ra /, r =. fm dσ/dp x (mb/(5 MeV c - A - )) b (fm) ~ ~ ~ ~ 8 8 ~ ~ E-dissipation is promoted for small b.

19 Contribution of impact parameter b-dependent PL distribution dσ/dp x (mb/(5 MeV c - A - )) b (fm) ~ ~ ~ ~ 8 8 ~ ~ Δσ/Δb (mb/fm) Δσ/Δb (mb/fm) High PL component Contribution of larger b is dominant. 8 b (fm) 8 b (fm) Low PL component Contribution of smaller b is dominant. 7 b-dependent PT distribution Δσ/Δb (mb/fm) Prod. rate vs. b Ar+ 9 Be Si + X b (fm) d σ/dp x dp y (mb/(mev c - A - ) ) b-dependent PT dist. - - b = ~ fm b = ~ fm b = ~ fm b = ~ 8 fm b = 8 ~ fm b = ~ fm The width of PT distribution is larger for P T (MeV/c) small b. v-dependent "T would be originated from contribution of impact parameters. 8-5

PT distribution at higher energy E = 95 MeV/u Ar + Be + X E = 9 MeV/u Ar + Al + X Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) -.x - Prod. rate /( Ar Acpt.)..8.... 5 (a) (b) - 5 5.

9 PT distribution with heavier target Dominant contribution of repulsive Coulomb force PT distribution of fragments 7 Ge( MeV/nucleon)+ 9 Be, 97 Au K. Meierbachtol et al.

20 PT distribution at higher energy E = 95 MeV/u Ar + Be + X E = 9 MeV/u Ar + Al + X Prod. rate /( Ar Acpt.) 5x - 5 (a) (b) -.x - Prod. rate /( Ar Acpt.) (a) (b) P L (MeV/c).x 9...x P L (MeV/c) Velocity dependence is not remarkable. 9 PT distribution with heavier target Dominant contribution of repulsive Coulomb force PT distribution of fragments 7 Ge( MeV/nucleon)+ 9 Be, 97 Au K. Meierbachtol et al., Phys. Rev. C 85() 8 9 Be 97 Au &A Deflection effect was observed as off-centered PT distribution. Deflection is remarkable for small &A reaction. Specified impact parameter can be defined for given isotope. Possibility to investigation proximity potential for heavy reaction system

21 Conclusions Remarkable correlation between width of PT distribution ("T) and fragment velocity (&PL) has been observed at E = 95 MeV/u.. Simple formulation : "T = k + k &PL. Comparison with previous results "T(&PL = ) = "GH Width of PL distribution "T at center of PL dist. = "D Conventionally used value. Important contribution of impact parameter to understand observed correlation Acknowledgements p78n@rips collaboration RCNP, Japan : I. Tanihata Tsukuba Univ., Japan : A. Ozawa The Enrico ermi Inst., USA : M. Notani RIKEN, Japan : K. Yoshida, K. Morimoto, A. Yoshida Saitama Univ., Japan : T. Yamaguchi Hitachi Co., Japan : T. Onishi KEK, Japan : Y. X. Watanabe IMP, China : Z. Liu, and RIKEN Ring Cyclotron staff and crew AMD calculation Tohoku Univ., Japan : A. Ono

arxiv:nucl-ex/ v1 23 Feb 2007

arxiv:nucl-ex/ v1 23 Feb 2007 Submitted to PRC Projectile fragmentation reactions and production of nuclei near the neutron drip-line M. Notani 1,, H. Sakurai 2,, N. Aoi 3, H. Iwasaki 2,, N. Fukuda 3, Z. Liu 3,, K. Yoneda 3, H. Ogawa