(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 209989, 6668]*) (*NotebookOutlinePosition[ 210917, 6697]*) (* CellTagsIndexPosition[ 210873, 6693]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ From Prakash notes, Chap. 3, giving a simplistic nuclear EoS for symmetric nuclear matter (N=z), eq. 3.8. (It is non-causal, however, giving a sound speed > c.) \ \>", "Text", FormatType->TextForm], Cell[CellGroupData[{ Cell["\<\ Date[] Off[General::spell1]\ \>", "Input"], Cell[BoxData[ \({2003, 9, 2, 14, 10, 28}\)], "Output"] }, Open ]], Cell["\<\ First, see if we can reproduce Table 3.1 from his formulas for the three parameters, sig=sigma, capB, and capA, eqs. 3.12-14.\ \>", "Text"], Cell[CellGroupData[{ Cell["n0 = 0.16 (* 1/fm^3 *)", "Input"], Cell[BoxData[ \(0.16`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["hbarc = 197.32 (* MeV*fm *)", "Input"], Cell[BoxData[ \(197.32`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["kF = (3 Pi^2 n0/2)^(1/3) (* 1/fm *)", "Input"], Cell[BoxData[ \(1.3330210137859972`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["kFMeV = kF * hbarc (* in MeV/c *)", "Input"], Cell[BoxData[ \(263.03170644025295`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["mnuc = 939.0 (* MeV *)", "Input"], Cell[BoxData[ \(939.`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["aveKE = (3/5) kFMeV^2 / (2 mnuc) (* MeV *)", "Input"], Cell[BoxData[ \(22.104050668649016`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["EbyA = mnuc - 16 (* MeV *)", "Input"], Cell[BoxData[ \(923.`\)], "Output"] }, Open ]], Cell["sig[K0_] := (1/9) (K0 + 2 aveKE)/(aveKE/3 - (EbyA - mnuc))", "Input"], Cell[CellGroupData[{ Cell["sig[200]", "Input"], Cell[BoxData[ \(1.1611697137234016`\)], "Output"] }, Open ]], Cell["\<\ capB[K0_] := (sig[K0]+1)*(aveKE/3 - (EbyA - \ mnuc))/(sig[K0]-1)\ \>", "Input"], Cell[CellGroupData[{ Cell["capB[200]", "Input"], Cell[BoxData[ \(313.3482662762763`\)], "Output"] }, Open ]], Cell["capA[K0_] := (EbyA - mnuc) - (5/3)*aveKE - capB[K0]", "Input"], Cell[CellGroupData[{ Cell["capA[200]", "Input"], Cell[BoxData[ \(\(-366.1883507240247`\)\)], "Output"] }, Open ]], Cell["\<\ This does indeed reproduce the first row of Table 3.1. The second row is\ \>", "Text"], Cell[CellGroupData[{ Cell["{capA[400], capB[400], sig[400]}", "Input"], Cell[BoxData[ \({\(-118.23172709227185`\), 65.3916426445235`, 2.1121371119094303`}\)], "Output"] }, Open ]], Cell["\<\ Now, to work out Prakash's eps[n] and p[n] to get the EoS. 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shown by Sanjay in his Zakopane lectures. It also looks like we could fit this nicely with something like a parabola. However, for pure neutron matter, we must also add the isospin symmetry (breaking) term which goes like (nneut - nprot)^2, as compared with our potential so far which goes like like the (sigma+1) power of n = nneut + nprot. Let's get that in first. Let x = proton fraction.\ \>", \ "Text"], Cell[CellGroupData[{ Cell["{nprot = x*n, nneut = (1-x)*n, Simplify[nneut+nprot]}", "Input"], Cell[BoxData[ \({n\ x, n\ \((1 - x)\), n}\)], "Output"] }, Open ]], Cell["\<\ Clear[n,u] u[n_] := n/n0\ \>", "Input"], Cell["From Prakash's eqs. 3.19-22", "Text"], Cell["avEF[n_] := (3/5)*(hbarc^2/(2*mnuc))*(3*Pi^2*n/2)^(2/3)", "Input"], Cell[CellGroupData[{ Cell["avEF[n0]", "Input"], Cell[BoxData[ \(22.10405066864902`\)], "Output"] }, Open ]], Cell["\<\ the value at n = n0 being same as aveKE calculated above, as it \ should.\ \>", "Text"], Cell["\<\ delEkin[n_,x_] := avEF[n]*( 2^(2/3)*((1-x)^(5/3) + x^(5/3)) - 1 )\ \ \>", "Input"], Cell[CellGroupData[{ Cell["delEkin[n,1/2]", "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell["also as it should be. 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No, ", StyleBox["not true", FontWeight->"Bold"], " for this case! 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(*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)