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This is "Proof" by Hal Clement (1942, Astounding). You can read it (with some OCR quirks) here.

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology.

All the elements you cite match, except for solar flares being ship launches. They do note that their cities "cool down the Sun for many thousands of units all around". The two starship captain-scientists are from Sirius and Sol.

This is "Proof" by Hal Clement (1942, Astounding). You can read it (with some OCR quirks) here.

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology.

All the elements you cite match, except for solar flares being ship launches. They do note that

our converters take so much as to lower the solar temperature considerably for thousands of miles around each city

The two protagonists are Kron, a ship-captain from Sol, and an unnamed scientist from Sirius B. The story recounts the disaster that befell Kron's friend Akro and matches your memories:

“In that moment, every one of us saw the identifying frequencies as the heat from Akro’s disrupted ship raised the substance which had trapped him to an energy level which permitted atomic radiation. Every one of us recognized the spectra of iron, of calcium, of carbon and silicon and a score of the other elements — Sirian, I tell you that that ‘trapping field’ was matter — matter in such a state that it could not radiate, and could offer resistance to other bodies in exactly the fashion of a solid. I thought, and have always thought, that some strange field of force held the atoms in their ‘solid’ positions; you have convinced me that I was wrong. The ‘field’ was the sum of the interacting atomic forces which you are trying to detect. The energy level of that material body was so low that those forces were able to act without interference. The condition you could not conceive of reaching artificially actually exists in nature!”

This is "Proof" by Hal Clement (1942, Astounding).

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology.

All the elements you cite match, except for solar flares being ship launches. They do note that their cities "cool down the Sun for many thousands of units all around". The two starship captain-scientists are from Sirius and Sol.

This is "Proof" by Hal Clement (1942, Astounding). You can read it (with some OCR quirks) here.

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology.

All the elements you cite match, except for solar flares being ship launches. They do note that their cities "cool down the Sun for many thousands of units all around". The two starship captain-scientists are from Sirius and Sol.

This is "Proof" by Hal Clement (1942, Astounding).

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology).

All the elements you cite match, except for solar flares being ship launches. They do note that their cities "cool down the Sun for many thousands of units all around". The two starship captain-scientists are from Sirius and Sol.

This is "Proof" by Hal Clement (1942, Astounding).

You can find it in The Great SF Stories IV, although I found it in Antologia Scolastica, an Italian anthology.

All the elements you cite match, except for solar flares being ship launches. They do note that their cities "cool down the Sun for many thousands of units all around". The two starship captain-scientists are from Sirius and Sol.