[PRad] [EXTERNAL] Transverse charge density and the radius of the proton

Sat Mar 5 13:41:30 EST 2022

Dear Douglas,

Thank you for your interest in our work and also for adding our results to
your plot!

Indeed, by making different choices when fitting (in our case, by choosing
different orders N of the form factor expansion) one can get quite
different radii. For this exact reason, we used cross-validation to
determine that the N = 5 fit provides the best balance between bias and
variance for the Mainz dataset. We also showed that adding regularization
to orders N > 5 bring them into agreement with the N = 5 fit.

Unfortunately, we don't have a bandwidth right now for studying other form
factor models, but we will make our full Python analysis code publicly
available in the next week or so. In fact, most of our code is already
available at https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_gramolin_radius&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=5kuVsVW-mdxj0QmhMt2rmt--z2C-AsXwrZOODj9gz-E&e= . In particular, the
function to calculate F_1 and F_2 that you asked for can be found in the
file "models.py" (function "calc_ffs"). Please let me know if you have any
questions about this code.

Your plot for the scattering-based radii is very comprehensive, and I can't
think of any results that you missed. I only noticed a typo in one of the
last names ("Graczky" instead of "Graczyk").

One final comment: I genuinely believe that our work is something more than
yet another fit of the Mainz data. We argue that the problem of
extrapolation to zero Q^2 can be avoided by considering the transverse
charge density and using the entire available Q^2 range. Moreover, we
suggest a simple and straightforward way of dealing with the bias-variance
trade-off. I hope that the scattering community considers these important
points rather than simply counting our numerical result as a "vote" for the
larger proton.

Best regards,
Alexander

On Sat, Mar 5, 2022 at 10:03 AM Douglas Higinbotham <doug at jlab.org> wrote:

>
>
> Dear Alexander,
>
>
>
> Thank you very much for the message.
>
>
>
> There was a paper we did a while ago that showed one can get a large or
> small radius from the full Mainz data set simply by varying analytic
> choices made in the fitting: https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.102.015205&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=rGlHtoBgWchLxV7vCHrHNAsEu7ZAUjvL0uTB6MaOyWg&e= 
>
>
>
>
> I was curious if your N=5 function (fit – true) would work with the “small
> radius” polynomial function found in that work as well as it does with the
> original Bernauer.   I can send you the numbers if you would like to try it.
>
>
>
> Also, could you send me your code for calculating your F1 and F2?    I use
> Python instead of Mathematica but it is usually straight forward to map one
> to the other.
>
>
>
> And finally, I have added your result to my list of electron scattering
> proton radius extractions.   For simplicity I have taken your three
> uncertainties in quadrature.  Of course, at this point CODATA-2014 is out
> of data as they have shifted to the uH point, but I keep it for reference.
>
>
>
>
>
> I have been trying make an unabridged list of the results, so please let
> me know if I am missing something.
>
>
>
> Best Wishes,
>
> Douglas
>
>
>
> p.s.
>
>
>
> Here is the list of references for the plot:
>
>
>
> "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_RevModPhys.35.335&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=EKC1QgA3aEZshLJylrIRJCiQhBjZ_zLtfyO-M5W80a8&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_RevModPhys.35.335&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=-MI4ZTWgo4-8HqJWibAuWcKNqwT7zv5q2mejl3ONr2g&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRev.141.1308&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=MmIIV_BZ1xrLxVlcmqI8qsvaoz0mGqHX4uThne-PviE&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRev.141.1308&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=_wTQBuZtWugwUNFtM8kcEwN4IbeSln4FjN96E1y1yrI&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=http-3A__www.jetp.ac.ru_cgi-2Dbin_dn_e-5F035-5F04-5F0651.pdf&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=4XCpo5KbhXusOlM2t6yh9dzHvru-8u07tKlcX8VMqpU&e= 
> <https://urldefense.proofpoint.com/v2/url?u=http-3A__www.jetp.ac.ru_cgi-2Dbin_dn_e-5F035-5F04-5F0651.pdf&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=hP1lR972uw1l90BZH6IegjrdfEzY_PxZaMRZMfYnpV0&e=>
> "
>    "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.9.2125&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=DvOj-jP44wnJGNfHj4FAfAxHItLbWoqi7l8RiT_sZqM&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.9.2125&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=5UsLzpqQy6CBmse_L3k4-gOUMJt35iTCTDwg18CanKo&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0550-2D3213-2875-2990514-2D3&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=d1gbqPI9UbP2AFnkuVTlKFKUlRpJMdHGLuEE9Vp4hRI&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0550-2D3213-2875-2990514-2D3&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=FeelKBbyEg7UA0V3ZT_fSVZMhhpLNxbTnvPDcVyThn0&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_BF01409496&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=sTEZDHzKifwGN_gNI6QL1E5T4h9tladVUgj-53xqlUs&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1007_BF01409496&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=GIFrrz8Zfz0YuZU4egHfAKfUrCf9L1hMEJrRCcCZ3jo&e=>
> "
>    "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0550-2D3213-2876-2990449-2D1&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=XbGHPC0XehdvnGSrgnlamtxwVA0ffKPFmpFdMwLSRk0&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0550-2D3213-2876-2990449-2D1&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=9tbEGXWJbxhg19EzBIqRKKWGj8PmgcNkKEQA1WwA7z4&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0375-2D9474-2880-2990104-2D9&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=ygBx_RRZ4CHPx1SpD-dEdV0-EpmOXqKAKI2hZhKx5DM&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0375-2D9474-2880-2990104-2D9&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=0xUXio7NDG9C-tbmlyODLYg131UkVTn6OAuQleIHBG4&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0168-2D583X-2891-2996079-2DZ&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=e8CiYxYmZmdtOdL0J8dY_c_iN0pBnysOITOKXgPD4kQ&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0168-2D583X-2891-2996079-2DZ&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=N-VUZkXxth18QYF3WFJ5I7oBkDBv-m5KWeQBv3T-wjk&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1142_S0218301394000255&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=99Df5704xo3UZyoetqxzLzmMdMas8o-jTJsJeVd9xFk&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1142_S0218301394000255&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=kz4OSqMV_4AOZc7oWA7W4V_sIeqrX1CMIeJnNRSZpbY&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0375-2D9474-2895-2900339-2D8&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=U_QqReCzbXvmEuZvm5W_ytnYsZykQ7Tng62yteZ6UN4&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_0375-2D9474-2895-2900339-2D8&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=locmhvR_FH3FJW2xauSxUcOR1pToroJNmOAEQHI1oqU&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_S0370-2D2693-2800-2900316-2D6&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=Cy8r6GXc6A_qkq8Mwbei8kIIXqY1EfrsZAN5YlTRa6M&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_S0370-2D2693-2800-2900316-2D6&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=eB0p-XuNNOg8ek_6skFocHatBs8N7B2M7row06m7zHE&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_S0370-2D2693-2801-2901285-2D0&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=2v2hTw4mw58U0XJrYc25-0Mp8dSFsYA2UgQd3Mrvn10&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_S0370-2D2693-2801-2901285-2D0&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=s-ii6vcsOG2AatXZPzW_IIB2YpH51cyrBJNxNZ3ARcM&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2003.09.092&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=AEUCE5Ye4KpoRr9oheeXMe2maivk_932RcImR5o1V2k&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2003.09.092&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=-CqiNiZCapDD6uZ_hoN6NY0uFLmsaQ-AXv4rvwNqIMs&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.70.068202&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=EAXCWkcLdS6nzUiMJJhO0ZP1VAsMvY0ZTVKXobhe3x4&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.70.068202&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=K4lFplIsB1Iub2pqPv8WiCc2vMDpXLQ7EbfP_-FSqIU&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.72.057601&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=c96zVMa-MaLGMlH0tMdnZcI4OWuQETl6jzmX4jNDKnc&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.72.057601&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=e2_ru_rjYVLGWjiA5WnAxCg_6dmhWpCXENiXRbGPXaU&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.75.035202&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=GNFUAqQfZGMu3C4rGjTEVbpmMWd_EyYLxIyA03pLT2E&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.75.035202&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=5V_1PSVai-Mcr5-OmQ768fCniJsnEYhpS0wX3IQB5qM&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevLett.105.242001&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=jy3tGCWG_bAg5KSN56-gz3AVtvrkxtvMXHvIsXt5yyo&e= 
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> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.82.113005&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=CnAd3pERfoF9zFplQzZ-BLQ9-2LFJkIDdyH17opc5UI&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.82.113005&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=kgwB2b3s6aMNniyzhcY7bYBmJMxrwO6rJR9iJpKAoeI&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.nuclphysa.2010.05.054&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=-RBtm99-mPKAXchixd5AuEXojIncVKl3FlLY6oVnDaQ&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.nuclphysa.2010.05.054&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=E_5s9XwPqFoauI1QoeXcPjHnoClMU5VytRYBgIxBuS8&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.84.055204&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=CEA_3QTo6Xf1-pDN0wn3_SJdgGPUzRhgf3Tg5xJRvLs&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.84.055204&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=xCcgjh32CnHvfpOtGK9VP4ngbOcBWHwqqkpI2uzET_o&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2011.10.002&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=UTFz8VclFHSqx8KtoLB2TNxiWb_zwzBx7dAGaZwyJXE&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2011.10.002&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=FiK_q3cCuqOiNjDGYMgQHXahY_JjRE39K8-eB166Neo&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.ppnp.2012.01.013&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=MsyuQke_RELCxAAt6PnKj_K6irwyeWH3pMXworm-d9o&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.ppnp.2012.01.013&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=KKy16hT8nVqk_C7co6wZWjqMXo4g51pLbGGMCIPiVBU&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.ppnp.2012.01.014&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=dNttxNUIkbdBA0MRqp8udVdG_1fjI3azYksas61VNSE&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.ppnp.2012.01.014&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=uzx2Dd-GwFfBfabr9zaGJ08uoTOo0Cvr58hY83JbHWE&e=>
> "
>    "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_i2012-2D12151-2D1&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=3xXtB7lGHkZVYOPlliLU7a8PMWGSkCFaFts9lUABOJE&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_i2012-2D12151-2D1&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=RuzABnDQN9oLqPCuSoHVSFWIzQyGg2kzV1t9VF4Av18&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.90.054334&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=IvtcEfHnSGcZ_gw4darwaRKh_o9EmM4BFSBuFS5mjQo&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.90.054334&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=a88BYaIXOPt8UKVSt-JDKzsxcMOVev773U7WAwGcYZ0&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.91.014023&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=QjCJ37jCmFLAig__Sz664U1NFm2NbR60hXBIleB2Rb8&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.91.014023&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=sP29LDhAybLtFTj20Hauw8RLQhdppeXiu9E8ZnFJzeU&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1063_1.4921430&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=NVjFYUoudyrt8_NbIut16RVcEgDYFb7BzuPoc5cxwIc&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1063_1.4921430&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=1aGt3w9ut1gNxfoxckm6bKa10u271C3ky25Hx69C4_A&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.92.013013&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=4buBcmwyR7L5v1GVWP6zMG5mk_oDtQd6-ibGWKkVq5U&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.92.013013&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=6-8rxYxsP5hYziuDnIFocRYa-K6i3yIzRpVJRkTx0gE&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.93.065207&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=Y0aJIQzb-FTKL2oo8CuQwR-ahWwH8OQieHic3NzcqTc&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.93.065207&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=9DQTi9ROTkq7OVTXncxhx596z5ynWNMVI2s1m8YUNqI&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.93.055207&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=VvcGWQD4bPYKM7gklT07JJM6odOI93AoiYDSLZ_7WG0&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.93.055207&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=fpbRZHG6F9z8hNyhKQIQLcacs8iKZRsGOGM2L5wCR9M&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.95.035203&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=i0ynREaOQaotDwSZU4I-HJ6cUP1WWivRuYvFhWlTEKs&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.95.035203&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=5uddKH1Rwb3WUWj1CTZj6XBsv5rGzf7lnx3UV9ErwyE&e=>"
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>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.99.044303&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=Tsd9qdSFs8DqpoE4MvRa0mMT-cTy3jQCaNMJbmALzqU&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.99.044303&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=EITKef73Of15dGxT8PDH0ggIGtgEBOEybzNEhxWJU9o&e=>"
>
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.99.055202&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=GIBTrUvFriIKQbGMrUF7maMb6Tp-OGDUk-aHDqadriY&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.99.055202&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=wT7daXzFQ7R1POTEcSyROW5ShlwfNe7eSFYoieumEl8&e=>"
>
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1038_s41586-2D019-2D1721-2D2&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=QeTDZcc9QWMMwXTmLi5ePgH7pX5U3sAeEr7Qabu4Wbc&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1038_s41586-2D019-2D1721-2D2&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=rHyQQdNaQcEMIM9GJvdrOmqJYni7qM7LQ6ssjfLrRjI&e=>"
>
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.102.035203&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=DxzVP7gYoPl319NtsHnfsFKPGmSzBG6YPOctpo7sLGA&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevC.102.035203&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=dthJAp69izSFr93e5vrHQE7L4u1VRABhkPnRMBFxzqo&e=>"
>
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.nuclphysa.2020.121767&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=bMaJp8IIFMRIwLLUzQWNYRiuCKRAfGxoun-3sdAXqJw&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.nuclphysa.2020.121767&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=YqZLtvoTWn9fORY6XIwRtXiMhxMBZ286Mh9lBBwCBdo&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_s10050-2D021-2D00414-2Dx&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=d0Bgt6Ws14mfTwlWZj29AvzP4QjXM7yre1hP9jBJFLM&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_s10050-2D021-2D00414-2Dx&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=zgRDOcgPoKeBTi_xMYDSC_CoMIwClyRzwzcrUKwjOdI&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_s10050-2D021-2D00389-2D9&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=_1rAGAXyKWWla0OOljOYdENIqTFnlLd87Gf2jX_AHL0&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1140_epja_s10050-2D021-2D00389-2D9&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=J5YpeNMTWJM03fRq5ru1qVw_dgcejFc_7iWUpWbjOi8&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2021.136254&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=q-RgZ98ibdw_aNpb5qquEX-lYrgB6_mKhon5oS-8wQA&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1016_j.physletb.2021.136254&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=lCyex4DnUX4OwxV5B0gAObJ7pJ4Z7ePFTwk3hHPGTLE&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_110.1103_PhysRevLett.127.092001&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=rFuXAWPQLrCn6auWjaLGp5uiv6LI8cCYQhIAAjBLxQg&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_110.1103_PhysRevLett.127.092001&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=T61STYnPJL-uxMUgZHUfDihWqO22G2D2Rk5UYY9kjZ0&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevLett.128.052002&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=JZS5tizOsri2sa4v9S21-xteqIZklHmTTCqsDUwrEt0&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevLett.128.052002&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=ekFbXe3xmM0xuaEIfx2Nx7H7rGbuqCpxs6yJ-ASCphE&e=>
> "
>   "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.105.054004&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=Y_Ppk_JqStwtUj9W1sYdeqkBd4swNXKVq1hZrC_fp4M&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.105.054004&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=aOuj1nKq9lTvbgpUN6cJ_A&m=NqF0uflvj-P1ctmnUc_jMk5kD8rJkOzRS_mOe0OXQ5Z2vUoFtfGVXBcphYQSTzge&s=ApbF_Oh8q5sJF8AZwdNlsqIJQanbdPGKOeuw9lpxlHo&e=>
> "
>
>
>
>
>
> *From: *PRad <prad-bounces at jlab.org> on behalf of Alexander Gramolin <
> gramolin at gmail.com>
> *Date: *Friday, March 4, 2022 at 5:04 PM
> *To: *"prad at jlab.org" <prad at jlab.org>
> *Subject: *[PRad] [EXTERNAL] Transverse charge density and the radius of
> the proton
>
>
>
> Dear Colleagues,
>
> I'd like to bring your attention to our latest research on the proton
> charge radius that has been published today in Physical Review D (see
> https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.105.054004&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=Y_Ppk_JqStwtUj9W1sYdeqkBd4swNXKVq1hZrC_fp4M&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1103_PhysRevD.105.054004&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=dfX8coqshXUbElaF_oWnz2EbQ4pNx-8RkX-tik-kc9NtcV2sQ9B2IF9LucQwSwqB&s=LK4nhe9UhLDNXS2iQ5dRecwP6GHu1fsdDtPyp2vdLzU&e=>).
> This result may be of some interest for the PRad-II experiment and
> analysis. Note that there are several new appendices compared to the
> preprint version posted on arXiv a year ago (
> https://urldefense.proofpoint.com/v2/url?u=https-3A__arxiv.org_abs_2102.13022&d=DwIFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=gt4fY0ZDFIuj_U71-8gnWvmjjJsPJx1Wv6gE-IQ7GDBzmYkx2pvRftK7Ky82e7Ys&s=86BVnWNrJGNGv3tFuQpM1mWdUYNeaiTtstZSs1gH_WU&e= 
> <https://urldefense.proofpoint.com/v2/url?u=https-3A__arxiv.org_abs_2102.13022&d=DwMFaQ&c=CJqEzB1piLOyyvZjb8YUQw&r=V3XNY-MaMKN2LuAaTdObrA&m=dfX8coqshXUbElaF_oWnz2EbQ4pNx-8RkX-tik-kc9NtcV2sQ9B2IF9LucQwSwqB&s=KZAfbfScAj9q5XWgFjWrYvNK7bH-U63zfwpCZ5hiaug&e=>).
> Please don't hesitate to contact me if you have any questions or comments.
>
> Best regards,
>
> Alexander Gramolin
>
>
>
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