,,

(上海理工大學(xué) 理學(xué)院,上海 200093)

在實(shí)驗(yàn)上研究重離子反應(yīng),需要用到重離子加速器,實(shí)驗(yàn)的成本很高,所以,通常用計(jì)算機(jī)模擬核反應(yīng).人們用QMD (量子分子動力學(xué))模型對重離子反應(yīng)進(jìn)行了大量的研究.Zhang等[17]利用改進(jìn)的QMD模型研究了重離子反應(yīng)中的同位素分布、中質(zhì)比、氚/氦3比等同位旋效應(yīng),采用多種Skyrme參數(shù)研究了同位旋擴(kuò)散、對稱能、核子有效質(zhì)量分裂與動量相關(guān)作用[18].李慶豐等[19]考慮了Skyrme勢能密度函數(shù),用極端相對論量子分子動力學(xué)(UrQMD)模型研究了197Au+197Au重離子碰撞中的自旋軌道耦合效應(yīng).Xie等[20]也對197Au+197Au的碰撞進(jìn)行了研究,發(fā)現(xiàn)對于中子-質(zhì)子有效質(zhì)量劈裂,中子-質(zhì)子差分集體流是一個有效的探針.郭文軍等用同位旋相關(guān)的QMD模型研究了12C與Al同位素的反應(yīng)截面[21],激發(fā)態(tài)56Ni反應(yīng)的原子核阻止[22],重離子反應(yīng)中由中子-質(zhì)子軔致輻射產(chǎn)生的光子以及它與對稱勢的關(guān)系[23],光核反應(yīng)中的核子發(fā)射數(shù)及其與截面的關(guān)系[24].

本文與前人工作的最大的區(qū)別是利用同位旋相關(guān)的QMD模型對中能重離子反應(yīng)進(jìn)行模擬,通過修改動量相關(guān)勢,得出不同的中子-質(zhì)子有效質(zhì)量劈裂的值,根據(jù)這些不同的值來研究其對原子核阻止、核子發(fā)射數(shù)的影響,并與實(shí)驗(yàn)上測定的原子核阻止和核子發(fā)射數(shù)進(jìn)行比較.這樣的研究不僅可以確定有效質(zhì)量劈裂值,而且可以給出其與原子核阻止、核子發(fā)射數(shù)的關(guān)聯(lián)性.

1 模 型

利用量子分子動力學(xué)[25-28]模型來模擬重離子反應(yīng).為了考慮同位旋效應(yīng)對重離子反應(yīng)過程的影響,對傳統(tǒng)的量子分子動力學(xué)模型作了適當(dāng)?shù)男薷?密度相關(guān)的平均場的計(jì)算需要考慮質(zhì)子和中子的區(qū)別(庫侖勢和對稱勢),計(jì)算核子-核子反應(yīng)截面和泡利阻塞時(shí)也要區(qū)分質(zhì)子和中子.通過這些修改,得到了改進(jìn)的同位旋相關(guān)的量子分子動力學(xué)(IQMD)[29]模型,它的平均場勢能U的表達(dá)式為

U=USky+UYuk+UCoul+UMDI+UPauli+Usym

(1)

動量相關(guān)作用UMDI可表示為[31]

(2)

式中:ρ0=0.16 fm-3表示原子核飽和密度;ρ表示原子核密度;t4,t5為參數(shù);p1-p2表示兩粒子的動量差.

中子-質(zhì)子有效質(zhì)量劈裂描述的是中子、質(zhì)子的勢能在動量方向上的梯度差.原有的QMD模型動量相關(guān)的部分沒有考慮中子和質(zhì)子的差別,所以,無法研究有效質(zhì)量劈裂對反應(yīng)的影響.本文在動量相關(guān)作用中引入了中子、質(zhì)子的差別,將式(2)修改為同位旋相關(guān)的動量相關(guān)作用.

(3)

(4)

式中:Un,Up分別為同位旋相關(guān)的中子、質(zhì)子的動量相關(guān)作用勢;t4,t5n,t5p為參數(shù).

中子、質(zhì)子的費(fèi)米動量[14]

(5)

(6)

當(dāng)有效質(zhì)量劈裂的平均值取0.31δ,0.41δ,0.51δ時(shí),根據(jù)要求計(jì)算不同密度、不同相對中子過剩下的有效質(zhì)量劈裂值,繼而確定t4,t5n,t5p的值.通過調(diào)整t4,t5n,t5p的值,增加動量相關(guān)的勢能部分,再調(diào)整對稱勢的強(qiáng)度系數(shù)c的值,使對稱勢部分相應(yīng)地減少相同的量,使整個核在飽和點(diǎn)密度附近的對稱能恢復(fù)到原始狀態(tài),這樣,整個核勢仍舊滿足各種實(shí)驗(yàn)所約束的條件.不同參數(shù)和有效質(zhì)量劈裂的值如表1所示.

表1 不同參數(shù)和有效質(zhì)量劈裂的值Tab.1 Different parameters and the values of the effective mass splitting

在圖1中,由上部分的圖可以看出,兩核子動量差Δp很大時(shí),6條線幾乎重疊在一起,這是因?yàn)楹俗芋w系能量較大,起主導(dǎo)作用,有效質(zhì)量劈裂所帶來的能量差異相對于系統(tǒng)的能量差異可以忽略不計(jì).兩核子的動量差不大時(shí)(12～22 MeV),動量相關(guān)作用對其影響最明顯.其中,有效質(zhì)量劈裂為0.31δ時(shí)的動量相關(guān)作用最大,有效質(zhì)量劈裂為0.51δ時(shí)的動量相關(guān)作用最小.進(jìn)一步研究了有效質(zhì)量劈裂帶來的動量相關(guān)作用的同位旋效應(yīng),圖1的下部分表明,兩核子動量差很小時(shí)(12 MeV以下),動量相關(guān)作用所引起的對稱能的變化很小,有效質(zhì)量劈裂對動量相關(guān)作用的同位旋效應(yīng)影響很小.兩核子動量差較大時(shí),動量相關(guān)作用所引起的對稱能的變化很大,有效質(zhì)量劈裂對動量相關(guān)作用的同位旋效應(yīng)影響越來越強(qiáng).也就是說,有效質(zhì)量劈裂通過對稱能的不同來影響核反應(yīng)的狀態(tài).有效質(zhì)量劈裂越大,中子和質(zhì)子的動量相關(guān)作用差別越大,即對稱能越大,動量相關(guān)作用的同位旋效應(yīng)越明顯.所以,有效質(zhì)量劈裂與系統(tǒng)的對稱能緊密相關(guān),是描述動量相關(guān)作用的物理量.

圖1 不同有效質(zhì)量劈裂的中子、質(zhì)子勢能及其差值隨相對動量的變化Fig.1 Relationship between the neutron and proton potential energy and their difference variation with different effective mass splitting and relative momentum

圖2是參數(shù)t4,t5n,t5p選取適當(dāng)值時(shí),用表1所示的3套參數(shù)計(jì)算得到的有效質(zhì)量劈裂在0.31δ,0.41δ,0.51δ周圍隨密度和相對中子過剩的演化.由圖2可以看出,當(dāng)δ相同時(shí),隨著密度的增加,有效質(zhì)量劈裂的值先增加后減小.在δ=0.15時(shí)作一條橫線,可以看出,密度較高時(shí),有效質(zhì)量劈裂在0.31δ周圍時(shí),其變化最緩慢,在0.51δ周圍時(shí),其變化最劇烈.而在核反應(yīng)的壓縮過程中,密度可以達(dá)到飽和密度的2～3倍,所以,不同的有效質(zhì)量劈裂對壓縮過程影響很大.密度較低時(shí),有效質(zhì)量劈裂在0.51δ周圍時(shí)變化劇烈,會迅速降低為零,同位旋相關(guān)的動量相關(guān)作用對核反應(yīng)影響變?nèi)?而核反應(yīng)過程中的膨脹和碎裂過程正處于該密度范圍,所以,不同的有效質(zhì)量劈裂對碎片的形成影響很大.

圖2 有效值劈裂隨密度和相對中子過剩的演化Fig.2 Evolution of the effective mass splitting with the density and relative neutron excesses

2 結(jié)果與討論

原子核阻止R[2,32-33]是在重離子碰撞過程中決定反應(yīng)結(jié)果(終態(tài)產(chǎn)物)的一個重要物理量,可以用來描述同位旋自由度逐漸從非平衡向平衡過渡的過程[34],其具體形式為

(7)

從式(7)可以看出,原子核阻止反映了核子間碰撞的激烈程度.前面的研究表明,動量相關(guān)作用較大時(shí),原子核阻止較大[35].而有效質(zhì)量劈裂取不同值時(shí),其動量相關(guān)作用不同,所以,有效質(zhì)量劈裂會對原子核阻止產(chǎn)生影響.本文比較了不同的中子-質(zhì)子有效質(zhì)量劈裂對原子核阻止的影響.

圖3(見下頁)表示112Sn+112Sn,124Sn+124Sn和132Sn+132Sn分別在能量E=50,100,200 MeV/u反應(yīng)系統(tǒng)中原子核阻止隨反應(yīng)時(shí)間t的演化過程.圖中3條線分別表示中子-質(zhì)子有效質(zhì)量劈裂為0.31δ,0.41δ,0.51δ時(shí)的原子核阻止.由圖3可以清楚地看出,中子-質(zhì)子有效質(zhì)量劈裂的大小對原子核阻止有明顯的影響,無論何種反應(yīng)系統(tǒng),在低能且動量差Δp=12～22 MeV時(shí),中子-質(zhì)子有效質(zhì)量劈裂在0.31δ時(shí),原子核阻止R總是最大的.這是因?yàn)?由圖1可知,中子-質(zhì)子有效質(zhì)量劈裂在0.31δ時(shí)動量相關(guān)作用比較大,總的體系能量較大,截面降低,所以,原子核阻止變大.中子-質(zhì)子有效質(zhì)量劈裂為0.41δ和0.51δ時(shí),原子核阻止幾乎相同.根據(jù)圖1的上部分可以得到中子-質(zhì)子有效質(zhì)量劈裂為0.51δ時(shí),動量相關(guān)作用的絕對大小小,所以,原子核阻止較小.而從圖1的下部分可以得到,當(dāng)中子-質(zhì)子有效質(zhì)量劈裂為0.51δ時(shí),動量相關(guān)作用的中子-質(zhì)子的相對大小大,中子、質(zhì)子動量相關(guān)作用差越大,同位旋效應(yīng)越明顯,原子核阻止越大.影響原子核阻止的兩個因素相互競爭,所以,中子-質(zhì)子有效質(zhì)量劈裂為0.41δ和0.51δ時(shí),兩條曲線幾乎重疊在一起.中子-質(zhì)子有效質(zhì)量劈裂為0.31δ的絕對大小大于中子-質(zhì)子有效質(zhì)量劈裂為0.41δ和0.51δ的絕對大小,所以,動量相關(guān)作用的絕對大小的影響占主導(dǎo)地位,而中子、質(zhì)子動量相關(guān)作用的差的影響占從屬地位.能量為200 MeV時(shí),即能量較高時(shí),體系的能量遠(yuǎn)大于動量相關(guān)作用的能量時(shí),中子-質(zhì)子有效質(zhì)量劈裂對其原子核阻止影響很小,所以,在能量較高時(shí),有效質(zhì)量劈裂對原子核阻止影響很小.

圖4表示112Sn+112Sn,124Sn+124Sn和132Sn+132Sn分別在能量為50,100,200 MeV/u反應(yīng)系統(tǒng)中中子、質(zhì)子發(fā)射數(shù)隨有效質(zhì)量劈裂的變化.

圖3 不同有效質(zhì)量劈裂的原子核阻止R隨時(shí)間t演化過程Fig.3 Evolution of the nuclear stopping over time with different

圖4 中子、質(zhì)子發(fā)射數(shù)隨有效質(zhì)量劈裂的變化Fig.4 Evolution of the neutron numbers and proton numbers with the effective mass splitting

在圖4中可以明顯看出,反應(yīng)能量越高,中子和質(zhì)子發(fā)射數(shù)越多.在相同的能量下,有效質(zhì)量劈裂分別在0.31δ,0.41δ,0.51δ時(shí),中子和質(zhì)子發(fā)射數(shù)是依次遞減的.也就是說,中子、質(zhì)子發(fā)射數(shù)是隨著有效質(zhì)量劈裂的增加而減少的.同樣,由圖1的上部分可以看出,有效質(zhì)量劈裂越大,動量相關(guān)作用越小,總的能量越低,所以,中子、質(zhì)子發(fā)射數(shù)就少.從圖4的任意一張圖中可以看到,兩條曲線中間的間隔相差不大,也就是說,中子發(fā)射數(shù)與質(zhì)子發(fā)射數(shù)的差幾乎保持不變,不同的有效質(zhì)量劈裂對其發(fā)射的相對大小影響較小.有效質(zhì)量劈裂對中子、質(zhì)子發(fā)射數(shù)的影響同時(shí)增加,同時(shí)減少.反應(yīng)系統(tǒng)能量越高時(shí),中子、質(zhì)子發(fā)射數(shù)的兩條線的間隔越來越寬,所得結(jié)論和文獻(xiàn)[36]相同.

3 結(jié) 論

通過修改QMD模型中的初始化程序,分析了中子-質(zhì)子有效質(zhì)量劈裂對中能重離子反應(yīng)的影響.利用同位旋相關(guān)的QMD模型對中能重離子反應(yīng)進(jìn)行了模擬,在前人經(jīng)驗(yàn)的基礎(chǔ)上,通過修改動量相關(guān)勢得出不同的有效質(zhì)量劈裂,從而完善中能重離子碰撞的輸運(yùn)理論.通過對上述問題的模擬計(jì)算研究,可以得出以下的結(jié)論:

a.中子-質(zhì)子有效質(zhì)量劈裂對原子核阻止R有很明顯的影響.動量相關(guān)作用的相對大小和絕對大小相互競爭,共同作用到原子核阻止上.中子-質(zhì)子有效質(zhì)量劈裂值不同時(shí),在高能時(shí)原子核阻止幾乎重合,在低能時(shí)差別較大,因此,建議選取低能情況來研究有效質(zhì)量劈裂對核反應(yīng)的影響.

b.中子-質(zhì)子有效質(zhì)量劈裂對中子、質(zhì)子發(fā)射數(shù)有很明顯影響.隨著中子-質(zhì)子有效質(zhì)量劈裂的增加,會使中子、質(zhì)子發(fā)射數(shù)減少.

c.可以通過實(shí)驗(yàn)上測得的原子核阻止和中子、質(zhì)子發(fā)射數(shù),得到與中子-質(zhì)子的有效質(zhì)量劈裂相關(guān)的信息.

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